Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33657 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33658 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#481 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
534 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)(14,15,20,25)(16,21,27,43)(17,30,31,65)(18,34,39,70)(19,40,37,24)(22,46,47,32)(23,49,52,38)(26,54,55,64)(28,59,35,69)(29,62,58,45)(33,51,41,66)(36,48,68,53)(42,67,73,56)(44,72,50,61)(57,75,63,77)(60,74,71,76);(14,16)(15,21)(17,26)(18,35)(19,29)(20,27)(22,42)(23,50)(24,45)(25,43)(28,39)(30,64)(31,55)(32,67)(33,57)(34,69)(36,71)(37,58)(38,72)(40,62)(41,63)(44,52)(46,56)(47,73)(48,74)(49,61)(51,77)(53,76)(54,65)(59,70)(60,68)(66,75);(14,17,19,41,20,31,37,33)(15,22,24,53,25,47,40,48)(16,26,29,63,27,55,58,57)(18,36,38,46,39,68,49,32)(21,42,45,76,43,73,62,74)(23,51,34,65,52,66,70,30)(28,60,61,67,35,71,72,56)(44,75,59,64,50,77,69,54);(16,27)(21,43)(26,55)(28,35)(29,58)(42,73)(44,50)(45,62)(54,64)(56,67)(57,63)(59,69)(60,71)(61,72)(74,76)(75,77)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26646);