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×#18407 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3493 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
904 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)(30,31,36,33)(32,39,43,45)(34,38,35,44)(37,41,40,42);(14,16)(15,19)(17,26)(18,23)(20,28)(21,29)(22,25)(24,27)(30,32)(31,37)(33,40)(34,42)(35,41)(36,43)(38,45)(39,44);(30,33,36,31)(32,40,43,37)(34,44,35,38)(39,41,45,42);(15,20)(16,23)(21,25)(24,26)(30,34,36,35)(31,38,33,44)(32,41,43,42)(37,39,40,45)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11395);