Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62867 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6758 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24)(17,22)(18,20)(19,23)(21,26)(25,34)(27,38)(28,37)(29,32)(30,33)(31,39)(35,41)(36,43)(40,45)(42,44);(15,20)(16,25)(17,28)(22,36)(23,33)(26,39)(27,42)(29,43)(32,37)(35,38)(40,41)(44,45);(14,16)(15,21)(17,27)(18,25)(19,26)(20,31)(22,35)(23,24)(28,41)(29,40)(30,39)(32,44)(33,34)(36,45)(37,38)(42,43);(15,20)(16,26)(21,34)(22,32)(23,33)(24,31)(25,39)(27,41)(35,45)(36,37)(38,44)(40,42);(14,17,18,29)(15,22,20,32)(16,27,25,40)(19,28,30,43)(21,35,31,44)(23,37,33,36)(24,38,34,45)(26,41,39,42);(15,23)(20,33)(21,24)(22,37)(31,34)(32,36)(35,38)(44,45)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55855);