Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61060 |
| 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 | |
2686 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)(22,36)(23,26)(24,31)(27,37)(29,44)(30,40)(32,39)(33,47)(34,48)(35,42)(38,46)(41,45)(43,49);(18,20,23,32)(19,24,26,40)(21,33,35,29)(22,30,37,31)(25,41,42,38)(27,39,36,28)(34,46,49,45)(43,44,48,47);(15,17)(18,21,23,35)(19,25,26,42)(20,29,32,33)(22,34,37,49)(24,38,40,41)(27,43,36,48)(28,44,39,47)(30,45,31,46);(20,30)(22,37)(24,39)(27,36)(28,40)(29,45)(31,32)(33,46)(34,49)(38,47)(41,44)(43,48);(19,26)(24,40)(25,42)(27,36)(28,39)(38,41)(43,48)(44,47)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54048);