Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42×C13 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×C13×#2873 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator | C2 | C23×C42×C13 |
| Frattini, cosocle | C2×C4 | C25×C13 |
| socle | C23×C13 | C23×C4 |
| prime radical | C25×C13 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
3342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35);(7,8,10,14,11,13,17,20)(9,12,16,19,15,18,21,22);(3,4,5,6)(7,9)(8,12)(10,16)(11,15)(13,18)(14,19)(17,21)(20,22);(9,15)(12,18)(16,21)(19,22);(8,13)(12,18)(14,20)(19,22)1768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53042);