Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12945 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19)(20,31)(21,25)(22,40)(23,41)(24,30)(26,33)(27,36)(28,39)(29,38)(32,45)(34,44)(35,47)(37,46)(42,43)(48,49);(14,16,17,15)(19,25)(21,36)(22,39)(23,38)(26,43)(27,29)(28,30)(31,45)(32,33)(34,42)(37,49)(40,41)(44,46)(47,48);(18,20)(19,26)(21,37)(22,32)(23,42)(24,35)(25,43)(27,47)(28,44)(29,48)(30,46)(31,40)(33,39)(34,38)(36,49)(41,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5933);