Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61090 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#532 ◁ G | |
2714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,24,29)(20,30,34,47)(21,26,37,45)(22,28,23,27)(25,39,42,33)(31,41,35,49)(32,40,48,43)(36,46,38,44);(18,20,24,34)(19,25,29,42)(21,35,37,31)(22,33,23,39)(26,43,45,40)(27,30,28,47)(32,38,48,36)(41,46,49,44);(15,17)(18,21)(19,26)(20,31)(22,38)(23,36)(24,37)(25,40)(27,46)(28,44)(29,45)(30,41)(32,33)(34,35)(39,48)(42,43)(47,49);(18,21)(19,26)(20,32)(22,36)(23,38)(24,37)(25,41)(27,44)(28,46)(29,45)(30,40)(31,33)(34,48)(35,39)(42,49)(43,47);(18,22,24,23)(19,27,29,28)(20,33,34,39)(21,36,37,38)(25,30,42,47)(26,44,45,46)(31,48,35,32)(40,49,43,41)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54078);