Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C2×C42 |
| direct product | C13×#17306 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(16,20)(19,21)(23,26)(24,28)(30,31,34,32)(33,35,37,36)(40,44)(42,45);(15,18)(19,21)(23,26)(24,28)(31,32)(33,37)(38,39,41,43)(40,45,44,42);(14,15,17,18)(16,19,20,21)(22,23,25,26)(24,27,28,29)(30,32,34,31)(33,35,37,36)(38,40,41,44)(39,42,43,45);(14,16)(15,19)(17,20)(18,21)(22,24)(23,27)(25,28)(26,29)(30,33,34,37)(31,35,32,36)(38,39)(40,42)(41,43)(44,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10294);