Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C2×C13×#1526 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C23×C13 | C2×C22⋊C4 |
| prime radical | C24×C13 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C22×C42×C13 ◁ G | |
1122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31);(4,8,9,10)(11,12,15,18,16,13,14,17);(3,4)(5,8)(6,10)(7,9)(11,13,16,12)(14,18,15,17);(3,5,7,6)(4,8,9,10)(11,14,16,15)(12,17,13,18)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10625);