Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33857 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | D4×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C13×#443 ◁ G | |
646 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)(16,28,33,63)(17,34,38,59)(18,39,44,57)(19,26,20,25)(22,47,51,31)(23,45,54,37)(24,42,58,43)(29,49,35,72)(30,48,69,52)(32,70,46,55)(36,73,74,53)(40,60,64,50)(41,56,75,77)(61,67,76,66)(62,68,71,65);(14,16)(15,22)(17,35)(18,40)(19,32)(20,46)(21,33)(23,52)(24,55)(25,50)(26,60)(27,51)(28,39)(29,38)(30,36)(31,43)(34,71)(37,67)(41,68)(42,47)(44,64)(45,66)(48,54)(49,53)(56,76)(57,63)(58,70)(59,62)(61,77)(65,75)(69,74)(72,73);(14,17)(15,23)(16,29)(18,36)(19,45)(20,37)(21,38)(22,48)(24,53)(25,59)(26,34)(27,54)(28,61)(30,64)(31,65)(32,67)(33,35)(39,56)(40,69)(41,43)(42,75)(44,74)(46,66)(47,68)(49,70)(50,71)(51,52)(55,72)(57,77)(58,73)(60,62)(63,76);(14,17)(15,23)(16,30)(18,41)(19,37)(20,45)(21,38)(22,49)(24,56)(25,34)(26,59)(27,54)(28,62)(29,64)(31,66)(32,68)(33,69)(35,40)(36,43)(39,53)(42,74)(44,75)(46,65)(47,67)(48,70)(50,76)(51,72)(52,55)(57,73)(58,77)(60,61)(63,71)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26845);