Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13126 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #124 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1924 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
300 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)(14,15,19,25,20,26,43,58,21,27,44,59,18,24,29,46)(16,28,33,60,31,50,61,56,34,48,41,72,32,22,45,49)(17,35,39,68,38,55,62,57,40,53,42,73,37,23,51,54)(30,63,64,75,36,69,70,77,65,47,67,74,66,52,71,76);(14,16,29,61,18,32,44,33,21,34,43,45,20,31,19,41)(15,22,46,60,24,48,59,49,27,50,58,72,26,28,25,56)(17,36,51,67,37,30,42,70,40,66,62,64,38,65,39,71)(23,52,73,75,53,47,57,76,55,69,68,74,35,63,54,77);(14,17,18,37,21,40,20,38)(15,23,24,53,27,55,26,35)(16,30,31,36,34,65,32,66)(19,42,29,62,44,39,43,51)(22,47,28,52,50,63,48,69)(25,57,46,68,59,54,58,73)(33,67,61,71,41,64,45,70)(49,75,60,77,56,74,72,76)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6114);