Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12750 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#12750 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1786 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#576 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
928 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)(16,26,29,41)(17,31)(18,23)(19,25)(20,27,37,44)(21,28,38,30)(22,33)(24,35)(32,42,45,36)(34,39)(40,43);(14,16)(15,20)(17,32)(18,28)(19,29)(21,22)(23,36)(24,42)(25,37)(26,39)(27,43)(30,35)(31,41)(33,44)(34,45)(38,40);(14,16)(15,21)(17,27)(18,30)(19,29)(20,22)(23,41)(24,26)(25,38)(28,35)(31,36)(32,43)(33,45)(34,44)(37,40)(39,42)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5738);