Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#12987 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #121 |
| 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)(14,15,19,26,20,27,41,56,21,24,42,43,18,25,38,53)(16,22,31,46,30,45,62,72,29,47,39,54,36,51,67,74)(17,32,35,65,34,50,66,55,33,52,40,68,37,23,48,49)(28,57,59,75,60,44,69,71,61,64,63,77,58,70,76,73);(14,16,19,39,20,30,41,67,21,29,42,31,18,36,38,62)(15,22,43,46,27,45,53,72,24,47,26,54,25,51,56,74)(17,28,40,59,34,60,48,69,33,61,35,63,37,58,66,76)(23,44,49,73,32,64,65,75,50,70,55,71,52,57,68,77);(14,17)(15,23)(16,28)(18,37)(19,40)(20,34)(21,33)(22,44)(24,50)(25,52)(26,55)(27,32)(29,61)(30,60)(31,63)(35,42)(36,58)(38,66)(39,59)(41,48)(43,49)(45,64)(46,73)(47,70)(51,57)(53,65)(54,71)(56,68)(62,76)(67,69)(72,75)(74,77)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5975);