Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#21777 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2308 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C24 | C24×C13 |
| prime radical | C13×#3485 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C24×C13 ◁ G | |
1318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
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)(16,24,27,20)(17,21)(18,30,31,22)(19,23)(25,32,39,34)(26,33)(28,41,42,35)(29,36)(37,40)(38,44)(43,45);(14,16)(15,20)(17,25)(18,26)(19,27)(21,34)(22,33)(23,24)(28,38)(29,39)(30,37)(31,40)(32,36)(35,44)(41,43)(42,45);(14,17,19,29)(15,21,23,36)(16,25,27,39)(18,28,31,42)(20,32,24,34)(22,35,30,41)(26,38,40,45)(33,43,37,44);(14,18)(15,22)(16,26)(17,28)(19,31)(20,33)(21,35)(23,30)(24,37)(25,38)(27,40)(29,42)(32,43)(34,44)(36,41)(39,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14765);