Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#32850 |
| 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 ◁ C43×C13 ◁ G | |
604 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)(15,16)(19,20)(22,23,25,26)(24,27,29,28)(30,31,34,37)(32,38,40,35)(33,36,42,45)(39,44,41,43);(14,15,18,16)(17,19,21,20)(22,24,25,29)(23,27,26,28)(30,32,34,40)(31,35,37,38)(33,41,42,39)(36,44,45,43);(14,16,18,15)(17,19,21,20)(23,26)(24,28)(27,29)(33,42)(36,45)(39,41)(43,44);(14,17,18,21)(15,19,16,20)(24,29)(27,28)(30,33,34,42)(31,36,37,45)(32,39,40,41)(35,43,38,44)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25838);