Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ C4×Q64 |
190 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 67 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) = 20224 |
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)(80,82,83,81);(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)(84,86,88,98)(85,91,93,114)(87,102,104,134)(89,110,107,142)(90,112,108,100)(92,118,119,145)(94,123,121,147)(95,124,111,116)(96,125,126,101)(97,117,113,105)(99,122,129,103)(106,140,138,136)(109,115,141,143)(120,146,132,130)(127,133,131,139)(128,137,135,144);(80,81,83,82)(84,85,88,93)(86,96,98,126)(87,101,104,125)(89,109,107,141)(90,111,108,95)(91,113,114,97)(92,117,119,105)(94,122,121,103)(99,130,129,146)(100,131,112,127)(102,123,134,147)(106,139,138,133)(110,118,142,145)(115,140,143,136)(116,128,124,135)(120,137,132,144)Polycyclic presentation:
2^8,79|a^2=e,b^2=h,c^2=eh,d^2=fg,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,d^b=df,f^b=fg,g^b=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, 90151);