Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9946 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#9958 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,23)(16,24,26,28)(17,20,18,22)(21,27,29,25)(30,31)(32,35)(33,36)(34,37)(38,41)(39,42)(40,44)(43,45);(15,20)(17,18)(21,24)(22,23)(25,27)(28,29)(30,32,34,39)(31,35,37,42)(33,38,40,45)(36,43,44,41);(14,16)(15,21)(17,25)(18,27)(19,26)(20,28)(22,24)(23,29)(30,33)(31,36)(32,38)(34,40)(35,41)(37,44)(39,45)(42,43)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2946);