Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25147 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,22,31,23,21,24,26)(20,27,28,32,29,25,30,33);(15,17)(18,20,24,30,23,29,22,28)(19,25,26,32,21,27,31,33);(18,21,23,19)(20,25,29,27)(22,31,24,26)(28,32,30,33);(15,17)(18,22,23,24)(19,26,21,31)(20,28,29,30)(25,32,27,33)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18135);