Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | SD128×D79 |
| Fitting | C79×SD128 ⋊ C2 |
| Sylow | C79 ⋊ C2×SD128 |
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 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);(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)(81,87)(82,93)(83,94)(84,99)(85,103)(88,89)(90,118)(91,120)(92,109)(95,126)(96,129)(97,110)(98,106)(100,134)(101,114)(102,107)(104,117)(105,108)(111,131)(112,130)(113,116)(115,136)(119,143)(121,122)(123,127)(124,125)(128,142)(132,139)(133,138)(135,141)(137,140);(80,81,86,92)(82,87,97,109)(83,98,101,132)(84,102,104,135)(85,105,103,91)(88,110,113,93)(89,114,116,94)(90,117,119,99)(95,118,128,143)(96,120,127,108)(100,133,124,131)(106,137,139,122)(107,140,141,121)(111,142,138,126)(112,123,136,129)(115,125,130,134)1435 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90612);