Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62892 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62956 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6346 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(16,22)(20,23)(24,28)(27,29)(31,35)(33,41)(36,38)(39,45);(14,15,19,17)(16,20,22,23)(18,21,26,25)(24,27,28,29)(30,31,34,35)(32,38,40,36)(33,37,41,42)(39,44,45,43);(14,16)(15,20)(17,23)(18,24)(19,22)(21,27)(25,29)(26,28)(30,32,34,40)(31,36,35,38)(33,39,41,45)(37,43,42,44);(14,17,19,15)(16,23,22,20)(18,21,26,25)(24,27,28,29)(30,33)(31,37)(32,39)(34,41)(35,42)(36,43)(38,44)(40,45);(14,18,19,26)(15,21,17,25)(16,24,22,28)(20,27,23,29);(14,16)(15,20)(17,23)(18,24)(19,22)(21,27)(25,29)(26,28)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55944);