Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #62636 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#62637 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C23×D8 |
| commutator, Frattini, cosocle | C8 | C25×C13 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
2026 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26)(17,22)(18,34)(19,39)(20,23)(21,28)(24,37)(25,36)(27,51)(29,58)(30,52)(31,44)(32,61)(33,64)(35,49)(38,50)(40,48)(41,54)(42,57)(43,66)(45,63)(46,60)(47,56)(53,73)(55,76)(59,72)(62,71)(65,70)(67,74)(68,77)(69,75);(14,16,20,30)(15,21,23,42)(17,27,31,53)(18,35,38,66)(19,40,36,29)(22,41,44,67)(24,48,47,58)(25,49,39,43)(26,50,52,34)(28,56,57,37)(32,62,59,77)(33,65,60,55)(45,70,69,76)(46,71,64,68)(51,72,73,61)(54,75,74,63);(14,17)(15,22)(16,27)(18,32)(19,33)(20,31)(21,41)(23,44)(24,45)(25,46)(26,51)(28,54)(29,55)(30,53)(34,61)(35,62)(36,60)(37,63)(38,59)(39,64)(40,65)(42,67)(43,68)(47,69)(48,70)(49,71)(50,72)(52,73)(56,75)(57,74)(58,76)(66,77);(17,31)(22,44)(27,53)(32,59)(33,60)(41,67)(45,69)(46,64)(51,73)(54,74)(55,65)(61,72)(62,77)(63,75)(68,71)(70,76);(15,23)(21,42)(22,44)(24,47)(25,39)(26,52)(34,50)(41,67)(43,49)(45,69)(46,64)(48,58)(51,73)(61,72)(68,71)(70,76)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55625);