Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18393 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#534 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
910 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)(16,22)(17,25)(18,20)(19,24)(21,27)(23,29)(26,28)(30,31,35,38)(32,39,42,45)(33,37,34,43)(36,40,44,41);(14,16)(15,19)(17,26)(18,23)(20,28)(21,29)(22,25)(24,27)(30,32)(31,36)(33,41)(34,40)(35,42)(37,45)(38,44)(39,43);(30,31)(32,36)(33,37)(34,43)(35,38)(39,40)(41,45)(42,44);(15,20)(16,23)(21,25)(24,26)(30,33,35,34)(31,37,38,43)(32,40,42,41)(36,39,44,45)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11381);