Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32872 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2826 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
482 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)(14,15,20,25,21,27,19,26)(16,28,32,46,33,56,31,22)(17,34,38,23,39,49,37,50)(18,24,41,54,42,55,43,53)(29,44,35,47,61,70,60,57)(30,58,63,51,65,72,64,45)(36,52,40,48,66,74,67,75)(59,69,62,73,68,76,77,71);(14,16,19,31,21,33,20,32)(15,22,25,28,27,46,26,56)(17,35,37,29,39,60,38,61)(18,30,41,63,42,65,43,64)(23,47,49,70,50,57,34,44)(24,51,53,58,55,45,54,72)(36,62,40,68,66,77,67,59)(48,71,52,76,75,73,74,69);(14,17,21,39)(15,23,27,50)(16,29,33,61)(18,40,42,67)(19,38,20,37)(22,44,46,70)(24,52,55,74)(25,34,26,49)(28,57,56,47)(30,62,65,77)(31,35,32,60)(36,43,66,41)(45,71,51,73)(48,54,75,53)(58,76,72,69)(59,64,68,63);(14,18)(15,24)(16,30)(17,36)(19,43)(20,41)(21,42)(22,45)(23,48)(25,54)(26,53)(27,55)(28,58)(29,59)(31,64)(32,63)(33,65)(34,52)(35,62)(37,67)(38,40)(39,66)(44,69)(46,51)(47,73)(49,74)(50,75)(56,72)(57,71)(60,77)(61,68)(70,76)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25860);