Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13096 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1898 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| prime radical | C2×C13×2−1+4 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×2−1+4 ◁ G | |
624 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)(16,26,31,55)(17,32,35,51)(18,36,27,23)(19,24)(20,25)(21,29)(22,34,47,41)(28,57)(30,54,40,71)(33,66)(37,45)(38,65)(39,68,56,49)(42,52)(43,72,75,77)(44,62)(46,67)(48,70)(50,69)(53,63)(58,64,61,74)(59,73)(60,76);(14,16,27,29,20,31,18,37)(15,21,36,55,25,45,23,26)(17,28,33,61,35,60,38,58)(19,40,56,69,42,30,39,62)(22,43,46,73,47,75,48,53)(24,50,68,54,52,44,49,71)(32,64,65,57,51,74,66,76)(34,63,67,77,41,59,70,72);(14,17)(15,22)(16,28)(18,38)(19,41)(20,35)(21,43)(23,48)(24,51)(25,47)(26,53)(27,33)(29,61)(30,63)(31,60)(32,52)(34,42)(36,46)(37,58)(39,67)(40,59)(44,64)(45,75)(49,65)(50,74)(54,76)(55,73)(56,70)(57,71)(62,77)(66,68)(69,72)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6084);