Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33579 |
| 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 | |
718 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)(22,34)(23,38)(24,28)(25,31)(27,36)(30,45)(32,46)(33,44)(35,40)(37,48)(39,43)(41,49)(42,47);(14,15,16,17);(18,20)(19,25)(21,30)(22,35)(23,39)(24,32)(26,40)(27,43)(28,42)(29,34)(31,36)(33,47)(37,49)(38,41)(44,45)(46,48);(18,21,24,23)(19,26,28,38)(20,30,32,39)(22,33,37,36)(25,40,42,41)(27,34,44,48)(29,45,46,43)(31,35,47,49)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26567);