Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63041 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#63069 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6496 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
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)(17,27)(18,21)(19,23)(20,22)(25,26)(28,29)(30,31,36,35)(32,39,34,37)(33,38,43,42)(40,45,41,44);(14,16,21,20)(15,22,18,24)(17,25,23,28)(19,26,27,29)(30,32,36,34)(31,37,35,39)(33,41,43,40)(38,45,42,44);(14,17)(15,19)(16,25)(18,27)(20,28)(21,23)(22,26)(24,29)(30,33,36,43)(31,38,35,42)(32,40,34,41)(37,44,39,45);(14,18,21,15)(16,22,20,24)(17,27,23,19)(25,26,28,29)(30,34,36,32)(31,39,35,37)(33,41,43,40)(38,45,42,44);(14,19,21,27)(15,23,18,17)(16,26,20,29)(22,28,24,25)(30,31,36,35)(32,37,34,39)(33,38,43,42)(40,44,41,45);(14,20,21,16)(15,22,18,24)(17,28,23,25)(19,26,27,29)(30,35,36,31)(32,39,34,37)(33,42,43,38)(40,45,41,44)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56057);