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×#62841 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6624 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)(15,19)(20,25)(21,26)(27,29)(30,31,35,36)(32,39,34,37)(33,38,41,43)(40,45,42,44);(17,24)(21,26)(22,28)(27,29)(31,36)(33,41)(37,39)(40,42);(14,15)(16,20)(17,21)(18,19)(22,27)(23,25)(24,26)(28,29)(30,31)(32,37)(33,38)(34,39)(35,36)(40,44)(41,43)(42,45);(14,16,18,23)(15,20,19,25)(17,22,24,28)(21,27,26,29)(30,32,35,34)(31,37,36,39)(33,40,41,42)(38,44,43,45);(14,17,18,24)(15,21,19,26)(16,22,23,28)(20,27,25,29)(30,33)(31,38)(32,40)(34,42)(35,41)(36,43)(37,44)(39,45);(14,15)(16,20)(17,21)(18,19)(22,27)(23,25)(24,26)(28,29)(30,34,35,32)(31,39,36,37)(33,42,41,40)(38,45,43,44)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55829);