Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C32×C79 ⋊ C2 |
| Sylow | C79 ⋊ #13728 |
238 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 147 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,81,82,83)(85,92)(91,110)(93,113)(94,114)(95,109)(96,116)(102,131)(108,136)(111,138)(112,137)(115,132)(117,142)(118,143)(119,130)(129,146)(133,135);(84,86,97,120,89,100,122,140,107,128,141,147,134,145,104,125,88,99,121,144,106,127,105,126,90,101,123,139,103,124,87,98)(85,91,102,118,94,111,132,130,109,137,135,146,136,142,113,116,92,110,131,143,114,138,115,119,95,112,133,129,108,117,93,96);(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)(81,83)(84,85)(86,96)(87,102)(88,92)(89,108)(90,109)(91,98)(93,97)(94,103)(95,107)(99,116)(100,129)(101,130)(104,131)(105,135)(106,136)(110,125)(111,139)(112,140)(113,121)(114,134)(115,141)(117,120)(118,124)(119,128)(122,133)(123,132)(126,137)(127,146)(138,147)(142,144)(143,145)Polycyclic presentation:
2^8,79|b^2=df,c^2=eh,d^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fg,g^a=gh,i^a=i^785062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90574);