Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17577 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#17676 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| prime radical | C24×C13 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C42×C13 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,21,18,20,26,28)(16,22,23,29,24,19,25,27)(30,31)(32,40,42,45)(33,38)(34,39)(35,37)(36,41,44,43);(14,16,18,24)(15,19,20,22)(17,25,26,23)(21,29,28,27)(30,32)(31,36)(33,41)(34,43)(35,42)(37,44)(38,40)(39,45);(31,37)(36,44)(38,39)(40,45);(15,20)(19,22)(21,28)(27,29)(30,33,35,34)(31,38,37,39)(32,41,42,43)(36,40,44,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10664);