Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13442 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13443 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2054 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
378 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)(14,15,21,27)(16,28,33,63)(17,34,40,70)(18,25,43,60)(19,24,44,59)(20,45,42,26)(22,47,51,30)(23,52,57,37)(29,64,68,48)(31,50,41,61)(32,49,46,58)(35,71,65,76)(36,56,38,74)(39,54,73,55)(53,66,62,75)(67,69,72,77);(14,16)(15,22)(17,35)(18,41)(19,30)(20,46)(21,33)(23,53)(24,58)(25,28)(26,61)(27,51)(29,38)(31,43)(32,42)(34,69)(36,68)(37,67)(39,75)(40,65)(44,47)(45,50)(48,55)(49,59)(52,72)(54,64)(56,71)(57,62)(60,63)(66,73)(70,77)(74,76);(14,17,18,36,42,73,44,52,21,40,43,38,20,39,19,37)(15,23,24,54,45,74,60,70,27,57,59,55,26,56,25,34)(16,29,30,65,46,72,31,66,33,68,47,35,32,67,41,75)(22,48,28,62,61,77,49,76,51,64,63,53,50,69,58,71)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6431);