Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#32897 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×2−1+6 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
3512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,25,31)(20,32,36,53)(21,37,40,55)(22,28,42,52)(23,30,24,29)(26,43,48,35)(27,45,50,39)(33,46,61,72)(34,62,65,57)(38,67,70,74)(41,54,44,51)(47,64,73,63)(49,68,75,69)(56,59,66,60)(58,77,79,71)(76,78,81,80);(18,20)(19,26)(21,33)(22,34)(23,43)(24,35)(25,36)(27,46)(28,47)(29,53)(30,32)(31,48)(37,66)(38,58)(39,60)(40,61)(41,64)(42,65)(44,63)(45,59)(49,71)(50,72)(51,57)(52,73)(54,62)(55,56)(67,81)(68,80)(69,78)(70,79)(74,76)(75,77);(18,21,25,40)(19,27,31,50)(20,33,36,61)(22,38,42,70)(23,39,24,45)(26,46,48,72)(28,49,52,75)(29,37,30,55)(32,56,53,66)(34,58,65,79)(35,59,43,60)(41,68,44,69)(47,71,73,77)(51,74,54,67)(57,76,62,81)(63,78,64,80);(18,22)(19,28)(20,34)(21,38)(23,44)(24,41)(25,42)(26,47)(27,49)(29,54)(30,51)(31,52)(32,57)(33,58)(35,64)(36,65)(37,67)(39,69)(40,70)(43,63)(45,68)(46,71)(48,73)(50,75)(53,62)(55,74)(56,76)(59,80)(60,78)(61,79)(66,81)(72,77)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 25885);