Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18233 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3534 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1002 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)(14,15,18,22)(16,20,23,27)(17,19,25,21)(24,26,29,28)(30,31,34,37)(32,35,39,42)(33,36,40,43)(38,44,45,41);(15,19)(17,25)(20,26)(21,22)(24,29)(27,28)(30,32)(31,35)(33,38)(34,39)(36,41)(37,42)(40,45)(43,44);(14,16)(15,20)(17,24)(18,23)(19,26)(21,28)(22,27)(25,29)(30,33)(31,36)(32,38)(34,40)(35,41)(37,43)(39,45)(42,44);(16,23)(20,27)(24,29)(26,28)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11221);