Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #13618 |
290 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 107 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)(84,87,90,105)(85,92,96,95)(86,98,101,102)(88,103,109,139)(89,104,112,132)(91,113,116,115)(93,117,121,120)(94,118,123,110)(97,125,127,126)(99,128,130,134)(100,111,133,135)(106,136,124,140)(107,141,142,137)(108,138,129,147)(114,143,144,122)(119,145,146,131);(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)(84,86,90,101)(85,91,96,116)(87,102,105,98)(88,107,109,142)(89,111,112,135)(92,115,95,113)(93,119,121,146)(94,122,123,143)(97,124,127,106)(99,129,130,108)(100,132,133,104)(103,137,139,141)(110,114,118,144)(117,131,120,145)(125,136,126,140)(128,138,134,147);(80,81,82,83)(84,85)(86,97)(87,92)(88,106)(89,110)(90,96)(91,99)(93,108)(94,104)(95,105)(98,125)(100,131)(101,127)(102,126)(103,136)(107,122)(109,124)(111,119)(112,118)(113,128)(114,141)(115,134)(116,130)(117,138)(120,147)(121,129)(123,132)(133,145)(135,146)(137,144)(139,140)(142,143)Polycyclic presentation:
2^8,79|a^2=e,b^2=h,c^2=h,d^2=fg,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,c^b=ch,d^b=df,f^b=fg,g^b=gh,i^b=i^781768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90014);