Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C79×C22⋊C32 ⋊ C2 |
| Sylow | C79 ⋊ #7335 |
158 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 151 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 2 generators on 151 points:
(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)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,82)(81,84)(83,87)(85,86)(88,90)(89,96)(91,107)(92,110)(93,105)(94,103)(95,106)(97,120)(98,123)(99,118)(100,102)(101,119)(104,113)(108,131)(109,135)(111,138)(112,116)(114,132)(115,134)(117,126)(121,129)(122,144)(124,146)(125,137)(127,130)(128,143)(133,140)(136,150)(139,141)(142,148)(145,149)(147,151);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,81)(82,86,87,84)(83,85)(88,89,92,98,93,99,111,124,94,100,112,125,114,127,139,147,95,101,113,126,115,128,140,148,91,97,108,121,109,122,136,145)(90,102,104,129,105,130,133,149,103,119,131,123,132,143,150,146,106,120,110,137,134,144,138,151,107,96,116,117,135,118,141,142)Polycyclic presentation:
2^8,79|a^2=d,c^2=h,d^2=f,f^2=g,g^2=h,b^a=bc,c^a=ce,c^b=ch,d^b=deh,i^b=i^783196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 56908);