Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #7365 |
120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 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 — 2 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)(80,82)(81,87,88,103)(83,93)(84,94)(85,95)(86,92)(89,109,106,102)(90,104,107,125)(91,105,108,126)(96,113)(97,116)(98,117)(99,118)(100,114)(101,115)(110,131,128,123)(111,132,129,124)(112,127,130,140)(119,134)(120,135)(121,137)(122,136)(133,142,141,139)(138,143);(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)(80,81,83,89,84,90,97,110,85,91,98,111,99,112,121,133,86,88,96,106,100,107,119,128,101,108,120,129,122,130,138,141)(82,87,93,102,94,104,116,123,95,105,117,124,118,127,137,139,92,103,113,109,114,125,134,131,115,126,135,132,136,140,143,142)Polycyclic presentation:
2^8,79|a^2=d,b^2=e,d^2=f,f^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eh,c^b=ch,d^b=de,i^b=i^78,d^c=dh1768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 56972);