Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#33713 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C22×C13 | C22×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
834 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19)(20,29)(21,26)(22,36)(23,38)(24,28)(25,32)(27,30)(31,42)(33,48)(34,44)(35,41)(37,49)(39,46)(40,47)(43,45);(18,20,30,45,23,33,37,47,24,34,35,46,21,31,22,32)(19,25,36,42,26,39,41,44,28,40,49,48,38,43,27,29);(14,15,16,17);(18,21,24,23)(19,26,28,38)(20,31,34,33)(22,35,37,30)(25,39,40,43)(27,36,41,49)(29,42,44,48)(32,46,47,45)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26701);