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×#61053 |
| 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×#525 ◁ G | |
2666 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)(20,28)(21,25)(22,35)(23,26)(24,30)(27,38)(29,46)(31,44)(32,49)(33,45)(34,42)(36,40)(37,43)(39,48)(41,47);(18,20,23,31)(19,24,26,40)(21,32,34,48)(22,36,38,30)(25,41,42,46)(27,44,35,28)(29,37,47,33)(39,45,49,43);(15,17);(18,21,23,34)(19,25,26,42)(20,29,31,47)(22,37,38,33)(24,39,40,49)(27,45,35,43)(28,46,44,41)(30,48,36,32);(19,26)(24,40)(25,42)(27,35)(28,44)(39,49)(41,46)(43,45)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54041);