Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#32897 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×2−1+6 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
3512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,21,27)(16,28,32,49)(17,33,36,51)(18,24,38,48)(19,26,20,25)(22,39,44,31)(23,41,46,35)(29,42,57,68)(30,58,61,53)(34,63,66,70)(37,50,40,47)(43,60,69,59)(45,64,71,65)(52,55,62,56)(54,73,75,67)(72,74,77,76);(14,16)(15,22)(17,29)(18,30)(19,39)(20,31)(21,32)(23,42)(24,43)(25,49)(26,28)(27,44)(33,62)(34,54)(35,56)(36,57)(37,60)(38,61)(40,59)(41,55)(45,67)(46,68)(47,53)(48,69)(50,58)(51,52)(63,77)(64,76)(65,74)(66,75)(70,72)(71,73);(14,17,21,36)(15,23,27,46)(16,29,32,57)(18,34,38,66)(19,35,20,41)(22,42,44,68)(24,45,48,71)(25,33,26,51)(28,52,49,62)(30,54,61,75)(31,55,39,56)(37,64,40,65)(43,67,69,73)(47,70,50,63)(53,72,58,77)(59,74,60,76);(14,18)(15,24)(16,30)(17,34)(19,40)(20,37)(21,38)(22,43)(23,45)(25,50)(26,47)(27,48)(28,53)(29,54)(31,60)(32,61)(33,63)(35,65)(36,66)(39,59)(41,64)(42,67)(44,69)(46,71)(49,58)(51,70)(52,72)(55,76)(56,74)(57,75)(62,77)(68,73)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25885);