Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#12988 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #386 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1869 |
| prime radical | C13×#532 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C8×C13 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,25,20,23,37,40,21,24,38,42,18,35,27,44)(16,26,30,36,31,41,45,17,29,33,43,32,28,22,39,34);(14,16,27,39,18,28,38,43,21,29,37,45,20,31,19,30)(15,22,40,36,35,33,25,34,24,41,44,32,23,26,42,17);(14,17)(15,16)(18,36)(19,26)(20,32)(21,34)(22,27)(23,31)(24,29)(25,43)(28,35)(30,42)(33,38)(37,41)(39,40)(44,45)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5976);