Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6670 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)(21,28)(25,37)(26,33)(27,38)(29,36)(30,32)(31,40)(34,43)(35,41)(39,45)(42,44);(15,20)(16,25)(17,29)(22,35)(23,33)(27,42)(28,40)(30,41)(32,36)(34,38)(39,43)(44,45);(14,16,26,40)(15,21,33,37)(17,27,41,42)(18,25,19,28)(20,31,23,24)(22,34,35,45)(29,43,30,39)(32,44,36,38);(15,20)(21,31)(22,32)(23,33)(24,37)(34,44)(35,36)(38,45);(14,17,18,30)(15,22,20,32)(16,27,25,39)(19,29,26,41)(21,34,31,44)(23,36,33,35)(24,38,37,45)(28,43,40,42);(15,23)(20,33)(21,24)(22,36)(31,37)(32,35)(34,38)(44,45)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55814);