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×#63042 |
| 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)(17,23)(18,22)(19,21)(20,28)(25,34)(26,32)(27,38)(29,36)(30,37)(31,35)(33,41)(39,44)(40,43)(42,45);(14,16)(15,20)(17,27)(18,28)(19,26)(21,34)(22,24)(23,33)(25,31)(29,40)(30,41)(32,35)(36,44)(37,38)(39,42)(43,45);(15,21)(16,25)(20,24)(22,35)(23,36)(26,28)(27,39)(32,34)(33,38)(37,45)(40,41)(43,44);(15,22)(16,26)(20,32)(21,35)(23,37)(24,34)(25,28)(27,40)(33,43)(36,45)(38,44)(39,41);(14,17,18,30)(15,23,22,37)(16,27,28,41)(19,29,31,42)(20,33,24,38)(21,36,35,45)(25,39,26,40)(32,43,34,44);(17,29)(23,36)(27,40)(30,42)(33,44)(37,45)(38,43)(39,41)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56030);