Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C79×#1423 ⋊ C2 |
| Sylow | C79 ⋊ #13633 |
190 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 83 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:
(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)(84,87,91,90)(85,93,96,112)(86,99,103,102)(88,104,109,108)(89,105,111,107)(92,113,115,140)(94,116,117,136)(95,110,118,139)(97,119,122,134)(98,124,126,125)(100,127,131,130)(101,128,133,129)(106,135,137,138)(114,120,142,143)(121,132,144,147)(123,145,146,141);(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)(84,86,98,123,89,101,104,127,87,99,124,145,105,128,109,131,91,103,126,146,111,133,108,130,90,102,125,141,107,129,88,100)(85,92,106,121,95,114,136,134,112,140,138,147,139,143,117,122,96,115,137,144,118,142,116,119,93,113,135,132,110,120,94,97);(80,81,82,83)(84,85)(86,97)(87,93)(88,106)(89,110)(90,112)(91,96)(92,100)(94,98)(95,107)(99,119)(101,132)(102,134)(103,122)(104,135)(105,118)(108,138)(109,137)(111,139)(113,127)(114,141)(115,131)(116,124)(117,126)(120,123)(121,129)(125,136)(128,144)(130,140)(133,147)(142,145)(143,146)Polycyclic presentation:
2^8,79|a^2=e,b^2=df,c^2=h,d^2=fg,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^c=i^781558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90068);