Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#12979 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #120 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1869 |
| prime radical | C13×#575 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
456 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)(14,15,19,25,20,26,40,53,21,27,41,54,18,24,38,51)(16,22,30,44,29,43,60,71,31,45,62,73,36,49,66,75)(17,32,35,64,34,47,65,52,33,50,39,67,37,23,46,48)(28,55,58,76,59,42,68,70,56,63,61,77,57,69,74,72);(14,16,19,30,20,29,40,60,21,31,41,62,18,36,38,66)(15,22,25,44,26,43,53,71,27,45,54,73,24,49,51,75)(17,28,39,61,34,59,46,74,33,56,35,58,37,57,65,68)(23,42,52,72,32,63,67,76,47,69,48,70,50,55,64,77);(14,17)(15,23)(16,28)(18,37)(19,39)(20,34)(21,33)(22,42)(24,50)(25,52)(26,32)(27,47)(29,59)(30,61)(31,56)(35,41)(36,57)(38,65)(40,46)(43,63)(44,72)(45,69)(48,54)(49,55)(51,64)(53,67)(58,62)(60,74)(66,68)(70,73)(71,76)(75,77)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5967);