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×#63065 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6492 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)(17,19)(18,22)(20,21)(23,27)(25,29)(26,28)(30,31,36,37)(32,33,40,45)(34,38,35,39)(41,43,42,44);(15,21)(17,27)(22,24)(25,28)(31,37)(32,40)(38,39)(41,42);(14,16,20,18)(15,22,21,24)(17,25,27,28)(19,26,23,29)(30,32)(31,33)(34,41)(35,42)(36,40)(37,45)(38,43)(39,44);(14,17)(15,23)(16,25)(18,28)(19,21)(20,27)(22,29)(24,26)(30,33)(31,32)(34,43)(35,44)(36,45)(37,40)(38,41)(39,42);(14,18,20,16)(15,22,21,24)(17,28,27,25)(19,26,23,29)(30,34,36,35)(31,38,37,39)(32,41,40,42)(33,43,45,44);(14,19,20,23)(15,17,21,27)(16,26,18,29)(22,25,24,28)(30,35,36,34)(31,39,37,38)(32,42,40,41)(33,44,45,43)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56053);