Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7547 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 2 generators on 181 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56,70,110,59,73,111,161,86,122,165,181,132,167,81,117,61,75,113,163,87,123,136,169,90,126,166,180,133,168,82,118,62,76,114,164,88,124,134,148,84,120,153,150,102,146,79,92,58,72,97,147,83,119,80,116,60,74,112,162,78,115,57,71)(55,63,77,107,66,94,129,125,89,142,135,170,138,155,98,106,65,93,128,158,101,149,154,160,104,152,177,172,140,157,100,109,68,96,131,159,103,151,176,174,143,179,178,173,141,175,145,127,91,144,137,171,139,156,99,108,67,95,130,121,85,105,64,69);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55,58,65,62,68,61,91)(56,69,72,106,76,109,75,127)(57,77,79,128,82,131,81,137)(59,85,83,138,88,140,87,141)(60,89,84,104,90,143,86,67)(63,92,93,118,96,117,144,71)(64,97,98,114,100,113,145,70)(66,102,101,133,103,132,139,78)(73,121,119,170,124,172,123,173)(74,125,120,160,126,174,122,108)(80,135,134,177,136,178,111,130)(94,150,149,180,151,181,156,162)(95,116,142,148,152,169,179,161)(99,112,129,153,154,166,176,165)(105,147,155,164,157,163,175,110)(107,146,158,168,159,167,171,115)Polycyclic presentation:
2^8,53|a^2=d,b^2=ce,c^2=ef,d^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^523398 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57472);