Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C2×C13×#1612 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G | |
1156 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39);(4,8)(5,6)(9,10)(11,12,15,18)(13,16,20,23)(14,17,21,24)(19,25,26,22);(3,4)(5,8)(6,10)(7,9)(11,13)(12,16)(14,19)(15,20)(17,22)(18,23)(21,26)(24,25);(3,5,7,6)(4,8,9,10)(11,14,15,21)(12,17,18,24)(13,19,20,26)(16,22,23,25)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11107);