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×#63061 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6384 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)(14,15,20,19)(16,23,26,21)(17,27,18,22)(24,28,25,29)(30,31,35,33)(32,38,40,36)(34,41,42,37)(39,43,45,44);(14,16,20,26)(15,21,19,23)(17,24,18,25)(22,28,27,29)(30,32,35,40)(31,36,33,38)(34,39,42,45)(37,43,41,44);(14,17,20,18)(15,22,19,27)(16,24,26,25)(21,28,23,29)(30,33,35,31)(32,36,40,38)(34,41,42,37)(39,43,45,44);(14,16)(15,21)(17,24)(18,25)(19,23)(20,26)(22,28)(27,29)(30,34)(31,37)(32,39)(33,41)(35,42)(36,43)(38,44)(40,45);(14,18,20,17)(15,22,19,27)(16,25,26,24)(21,28,23,29);(14,19,20,15)(16,23,26,21)(17,27,18,22)(24,29,25,28)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56049);