Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33485 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C24 |
| commutator | C22 | C23×C8×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C22×C13 | C23×C8 |
| prime radical | C2×C13×#41 | C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ G | |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23,27,31,28,24,32,34,26,29,35,36,25,33,30,37);(15,18)(19,21)(23,29)(24,33)(31,36)(34,37);(22,24,27,34,28,29,32,36,26,33,35,37,25,23,30,31);(14,16,17,20)(15,19,18,21)(22,25,26,28)(23,24,29,33)(27,30,35,32)(31,34,36,37)1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26473);