Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62881 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6610 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)(14,15)(16,20)(17,24)(18,19)(21,25)(22,26)(23,29)(27,28)(30,31,36,38)(32,35,33,37)(34,39,43,45)(40,42,41,44);(16,22)(20,26)(23,28)(27,29)(30,32,36,33)(31,37,38,35)(34,41,43,40)(39,42,45,44);(15,19)(20,26)(21,24)(27,29)(31,38)(32,33)(39,45)(40,41);(14,15)(16,20)(17,21)(18,19)(22,26)(23,27)(24,25)(28,29)(30,33,36,32)(31,35,38,37)(34,41,43,40)(39,42,45,44);(14,16,18,22)(15,20,19,26)(17,23,25,28)(21,27,24,29)(30,34,36,43)(31,39,38,45)(32,40,33,41)(35,42,37,44);(14,17)(15,21)(16,23)(18,25)(19,24)(20,27)(22,28)(26,29)(30,35)(31,32)(33,38)(34,42)(36,37)(39,40)(41,45)(43,44)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55869);