Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61106 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61108 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
2592 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)(16,28)(17,33)(18,24)(19,27)(20,26)(21,25)(22,31)(23,35)(29,43)(30,55)(32,51)(34,63)(36,53)(37,68)(38,52)(39,49)(40,45)(41,50)(42,47)(44,60)(46,66)(48,61)(54,58)(56,69)(57,62)(59,70)(64,74)(65,72)(67,73)(71,76)(75,77);(14,16)(15,22)(17,29)(18,37)(19,40)(20,31)(21,32)(23,43)(24,48)(25,45)(26,51)(27,28)(30,38)(33,62)(34,64)(35,58)(36,59)(39,60)(41,61)(42,57)(44,50)(46,71)(47,70)(49,55)(52,68)(53,54)(56,65)(63,77)(66,75)(67,76)(69,73)(72,74);(14,17,21,36)(15,23,25,47)(16,29,32,59)(18,34,39,67)(19,35,20,42)(22,43,45,70)(24,46,49,72)(26,33,27,53)(28,54,51,62)(30,56,61,75)(31,57,40,58)(37,64,60,76)(38,65,41,66)(44,69,68,77)(48,71,55,74)(50,73,52,63);(14,18)(15,24)(16,30)(17,34)(19,41)(20,38)(21,39)(22,44)(23,46)(25,49)(26,52)(27,50)(28,55)(29,56)(31,60)(32,61)(33,63)(35,66)(36,67)(37,40)(42,65)(43,69)(45,68)(47,72)(48,51)(53,73)(54,74)(57,76)(58,64)(59,75)(62,71)(70,77);(15,25)(22,45)(23,47)(24,49)(26,27)(28,51)(33,53)(43,70)(44,68)(46,72)(48,55)(50,52)(54,62)(63,73)(69,77)(71,74)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54096);