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×#33860 |
| 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 | |
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)(14,15,22,28)(16,29,34,64)(17,35,24,50)(18,39,42,38)(19,43,48,59)(20,27,21,26)(23,51,55,32)(25,46,60,47)(30,31,36,69)(33,71,49,57)(37,67,56,41)(40,74,52,53)(44,61,76,54)(45,58,77,75)(62,63,68,66)(65,70,73,72);(14,16,22,34)(15,23,28,55)(17,36,24,30)(18,40,42,52)(19,44,48,76)(20,33,21,49)(25,57,60,71)(26,54,27,61)(29,59,64,43)(31,67,69,41)(32,46,51,47)(35,72,50,70)(37,74,56,53)(38,63,39,66)(45,68,77,62)(58,65,75,73);(14,17,22,24)(15,18,28,42)(16,30,34,36)(19,37,48,56)(20,39,21,38)(23,52,55,40)(25,41,60,67)(26,50,27,35)(29,62,64,68)(31,57,69,71)(32,65,51,73)(33,63,49,66)(43,45,59,77)(44,53,76,74)(46,58,47,75)(54,72,61,70);(14,18)(15,24)(16,31)(17,28)(19,45)(20,35)(21,50)(22,42)(23,53)(25,58)(26,39)(27,38)(29,63)(30,57)(32,70)(33,68)(34,69)(36,71)(37,59)(40,44)(41,47)(43,56)(46,67)(48,77)(49,62)(51,72)(52,76)(54,65)(55,74)(60,75)(61,73)(64,66)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26848);