Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33689 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#575 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C4×C13×M16 ◁ G | |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,23)(16,24,26,42)(17,29,30,45)(18,34,32,22)(20,35,37,27)(21,39,40,33)(25,41,28,44)(31,36,43,38);(17,30)(21,40)(24,42)(27,35)(29,45)(31,43)(33,39)(41,44);(14,16)(15,20)(17,31)(18,25)(19,26)(21,41)(22,36)(23,37)(24,29)(27,33)(28,32)(30,43)(34,38)(35,39)(40,44)(42,45);(16,25,26,28)(17,30)(20,36,37,38)(21,40)(24,41,42,44)(27,31,35,43)(29,45)(33,39)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26677);