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) = C2×C4 |
| direct product | C13×#13123 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #121 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1923 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
312 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)(14,15,19,25,20,24,40,43,21,26,41,50,18,39,28,54)(16,27,31,52,32,46,61,71,33,53,62,74,30,22,42,45)(17,34,37,65,38,64,66,75,36,23,47,49,35,48,55,68)(29,56,59,76,60,44,69,70,58,51,72,73,57,63,67,77);(14,16,28,42,18,30,41,62,21,33,40,61,20,32,19,31)(15,22,43,52,39,53,25,45,26,46,54,74,24,27,50,71)(17,29,55,67,35,57,47,72,36,58,66,69,38,60,37,59)(23,44,68,73,64,56,49,70,34,63,75,76,48,51,65,77);(14,17,18,35,21,36,20,38)(15,23,24,48,26,34,39,64)(16,29,30,57,33,58,32,60)(19,37,28,55,41,47,40,66)(22,44,27,51,46,63,53,56)(25,49,43,68,50,65,54,75)(31,59,42,67,62,72,61,69)(45,70,52,73,71,77,74,76)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6111);