Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13468 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #2065 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
304 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,46,21,28,45,27)(16,29,61,50,35,58,34,69)(17,36,47,57,42,71,41,54)(18,26,43,24,44,59,19,25)(22,48,51,31,52,33,67,32)(23,40,55,38,56,73,60,39)(30,49,64,77,65,76,70,75)(37,72,68,53,66,74,63,62);(14,16,18,31,20,34,43,48,21,35,44,32,45,61,19,33)(15,22,24,29,27,51,26,50,28,52,25,58,46,67,59,69)(17,37,38,65,41,68,40,70,42,66,39,30,47,63,73,64)(23,53,36,49,55,72,57,75,56,62,71,76,60,74,54,77);(14,17)(15,23)(16,30)(18,40)(19,39)(20,47)(21,42)(22,49)(24,57)(25,54)(26,36)(27,60)(28,56)(29,62)(31,37)(32,66)(33,68)(34,70)(35,65)(38,43)(41,45)(44,73)(46,55)(48,63)(50,72)(51,77)(52,76)(53,58)(59,71)(61,64)(67,75)(69,74)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6456);