Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C157 ⋊ #1855 |
278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 5024 |
A minimal faithful permutation representation — 3 generators on 177 points:
(1,2,6,12,22,36,54,76,102,132,103,73,97,125,145,112,80,52,72,96,124,137,107,81,59,41,27,13,3,7,15,25,39,57,79,105,135,152,133,99,127,147,118,86,58,34,50,70,94,122,142,113,87,65,43,23,9,17,29,45,63,85,111,140,154,156,150,129,144,116,90,64,40,20,32,48,68,92,120,146,119,89,61,37,19,31,47,67,91,117,130,149,155,157,153,139,110,84,62,44,26,10,18,30,46,66,88,114,143,115,83,55,33,49,69,93,121,136,100,128,148,151,134,104,78,56,38,24,14,4,8,16,28,42,60,82,108,138,109,77,51,71,95,123,141,106,74,98,126,131,101,75,53,35,21,11,5)(159,161);(2,4,5,3)(6,10,11,9)(7,8,14,13)(12,20,21,19)(15,18,24,23)(16,26,27,17)(22,34,35,33)(25,32,38,37)(28,40,41,31)(29,30,44,43)(36,52,53,51)(39,50,56,55)(42,58,59,49)(45,48,62,61)(46,64,65,47)(54,74,75,73)(57,72,78,77)(60,80,81,71)(63,70,84,83)(66,86,87,69)(67,68,90,89)(76,100,101,99)(79,98,104,103)(82,106,107,97)(85,96,110,109)(88,112,113,95)(91,94,116,115)(92,118,119,93)(102,130,131,129)(105,128,134,133)(108,136,137,127)(111,126,139,132)(114,141,142,125)(117,124,144,138)(120,145,146,123)(121,122,147,143)(135,149,151,150)(140,148,153,152)(154,155,157,156)(162,164,166,172,167,173,165,175)(163,168,169,176,170,177,174,171);(2,3,5,4)(6,9,11,10)(7,13,14,8)(12,19,21,20)(15,23,24,18)(16,17,27,26)(22,33,35,34)(25,37,38,32)(28,31,41,40)(29,43,44,30)(36,51,53,52)(39,55,56,50)(42,49,59,58)(45,61,62,48)(46,47,65,64)(54,73,75,74)(57,77,78,72)(60,71,81,80)(63,83,84,70)(66,69,87,86)(67,89,90,68)(76,99,101,100)(79,103,104,98)(82,97,107,106)(85,109,110,96)(88,95,113,112)(91,115,116,94)(92,93,119,118)(102,129,131,130)(105,133,134,128)(108,127,137,136)(111,132,139,126)(114,125,142,141)(117,138,144,124)(120,123,146,145)(121,143,147,122)(135,150,151,149)(140,152,153,148)(154,156,157,155)(158,159)(160,161)(162,163,166,169,167,170,165,174)(164,171,172,168,173,176,175,177)Polycyclic presentation:
2^7,157|a^2=f,b^2=f,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^28,d^b=dg,h^b=h^129,h^f=h^156818 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 20463);