Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1804 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
412 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)(16,26,29,43)(17,23)(18,22)(19,35)(20,25)(21,27,38,30)(24,33)(28,41,32,37)(31,39)(34,40)(36,45,42,44);(14,16)(15,21,25,38)(17,27)(18,32)(19,30)(20,29)(22,36,40,42)(23,26,35,43)(24,41,39,37)(28,34)(31,45)(33,44);(15,22)(17,19)(18,33)(21,36)(23,24)(25,40)(26,41)(27,30)(28,45)(31,34)(32,44)(35,39)(37,43)(38,42)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5814);