Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33618 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#466 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
656 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)(15,21)(16,27)(17,22)(18,19)(23,38)(24,34)(25,36)(26,35)(28,42)(29,32)(30,31)(33,40)(39,45)(41,44);(14,15,22,36,19,26,31,34,20,24,30,35,18,25,17,21)(16,23,37,38,27,40,42,44,29,39,43,45,32,41,28,33);(14,16)(15,23)(17,28)(18,32)(19,27)(20,29)(21,33)(22,37)(24,39)(25,41)(26,40)(30,43)(31,42)(34,44)(35,45)(36,38);(15,24)(21,34)(23,39)(25,26)(33,44)(35,36)(38,45)(40,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26606);