Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18263 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
948 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)(14,15,19,17)(16,24,28,40)(18,31,33,43)(20,22,35,29)(21,36,25,26)(23,38,30,34)(27,39,42,44)(32,37,45,41);(14,16,20,27)(15,21,22,37)(17,25,29,41)(18,32,34,26)(19,28,35,42)(23,39,31,24)(30,44,43,40)(33,45,38,36);(14,17)(15,19)(16,25)(18,23)(20,29)(21,28)(22,35)(24,26)(27,41)(30,33)(31,34)(32,39)(36,40)(37,42)(38,43)(44,45);(15,22)(17,29)(21,37)(23,31)(24,39)(25,41)(30,43)(40,44)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11251);