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×#62839 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6616 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)(32,41)(33,34)(35,43)(36,37)(38,42)(39,45)(40,44);(17,24)(21,26)(22,28)(27,29)(31,37)(32,42)(34,39)(40,43);(14,15)(16,20)(17,21)(18,19)(22,27)(23,25)(24,26)(28,29)(30,32)(31,38)(33,43)(34,44)(35,39)(36,42)(37,41)(40,45);(14,16,18,23)(15,20,19,25)(17,22,24,28)(21,27,26,29)(30,33)(31,39)(32,43)(34,37)(35,38)(36,45)(40,42)(41,44);(14,17,18,24)(15,21,19,26)(16,22,23,28)(20,27,25,29)(30,34,36,39)(31,33,37,45)(32,44,42,35)(38,43,41,40);(14,15)(16,20)(17,21)(18,19)(22,27)(23,25)(24,26)(28,29)(30,35,36,44)(31,40,37,43)(32,39,42,34)(33,38,45,41)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55827);