Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24985 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#24985 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2420 |
| prime radical | C13×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,28)(17,32)(18,22)(19,26)(20,25)(21,27)(23,35)(24,31)(29,44)(30,39)(33,41)(34,40)(36,42)(37,43)(38,45);(14,16,20,30,21,31,19,18)(15,22,26,24,27,39,25,28)(17,33,35,29,37,34,36,45)(23,40,32,44,42,41,43,38);(14,17)(15,23)(16,29)(18,34)(19,35)(20,36)(21,37)(22,38)(24,41)(25,32)(26,43)(27,42)(28,40)(30,33)(31,45)(39,44);(14,18,19,31,21,30,20,16)(15,24,25,22,27,28,26,39)(17,34,35,45,37,33,36,29)(23,41,32,38,42,40,43,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17973);