Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32481 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C4⋊C4 ◁ G | |
576 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)(14,15,17,18)(16,20,21,19)(22,23,26,28)(24,27,25,29)(30,31)(32,38)(33,36)(34,37)(35,40)(39,44)(41,43)(42,45);(15,18)(16,21)(22,24,26,25)(23,27,28,29)(30,32)(31,35)(33,40)(34,39)(36,38)(37,43)(41,42)(44,45);(22,25,26,24)(23,27,28,29)(32,39)(34,42)(35,43)(37,45)(38,44)(40,41);(14,16,17,21)(15,19,18,20)(23,28)(27,29)(31,36)(32,40)(37,45)(39,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25469);