Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24985 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#29154 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2563 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
612 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)(14,15,19,25)(16,22)(17,29,31,35)(18,21,20,24)(23,32,39,30)(26,34)(27,41)(28,36)(33,38)(37,40)(42,44)(43,45);(15,21,25,24)(16,26,28,33)(22,36)(23,35,39,29)(27,40,42,43)(34,38)(37,45)(41,44);(14,16)(15,22)(17,27)(18,26)(19,28)(20,33)(21,34)(23,37)(24,38)(25,36)(29,41)(30,40)(31,42)(32,43)(35,44)(39,45);(14,17,18,30,19,31,20,32)(15,23,24,29,25,39,21,35)(16,27,26,40,28,42,33,43)(22,37,38,41,36,45,34,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 22142);