Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33619 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#466 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3067 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
636 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)(16,28,31,54)(17,35,38,52)(18,39,41,50)(19,26,20,25)(22,43,45,32)(23,42,49,37)(24,40,51,29)(30,59,60,76)(33,56,34,55)(36,67,68,48)(44,71,72,77)(46,63,47,57)(53,64,75,62)(58,66,69,74)(61,65,70,73);(14,16,29,57,20,34,41,43,21,31,40,63,19,33,18,32)(15,22,39,56,26,47,51,54,27,45,50,55,25,46,24,28)(17,30,58,77,37,62,68,70,38,60,69,71,42,64,36,61)(23,44,66,59,35,65,67,75,49,72,74,76,52,73,48,53);(14,17)(15,23)(16,30)(18,36)(19,42)(20,37)(21,38)(22,44)(24,48)(25,52)(26,35)(27,49)(28,53)(29,58)(31,60)(32,61)(33,64)(34,62)(39,66)(40,69)(41,68)(43,70)(45,72)(46,73)(47,65)(50,74)(51,67)(54,75)(55,76)(56,59)(57,77)(63,71);(16,31)(22,45)(28,54)(30,60)(32,43)(33,34)(44,72)(46,47)(53,75)(55,56)(57,63)(59,76)(61,70)(62,64)(65,73)(71,77)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26607);