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×#62825 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6530 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)(17,24)(20,25)(23,28)(31,36)(32,40)(33,43)(39,44);(16,22)(20,25)(23,28)(27,29)(30,31,35,36)(32,41,40,37)(33,38,43,45)(34,44,42,39);(14,15,18,19)(16,20,22,25)(17,21,24,26)(23,27,28,29)(30,32,35,40)(31,37,36,41)(33,42,43,34)(38,44,45,39);(30,33)(31,38)(32,42)(34,40)(35,43)(36,45)(37,44)(39,41);(14,16)(15,20)(17,23)(18,22)(19,25)(21,27)(24,28)(26,29)(30,34,35,42)(31,39,36,44)(32,33,40,43)(37,38,41,45);(14,17)(15,21)(16,23)(18,24)(19,26)(20,27)(22,28)(25,29)(30,33)(31,38)(32,42)(34,40)(35,43)(36,45)(37,44)(39,41)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55813);