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×#61086 |
| 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 | |
2666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
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)(27,39)(29,37)(30,46)(32,44)(33,47)(34,45)(35,42)(38,43)(40,49)(41,48);(18,20,23,32)(19,24,26,29)(21,33,35,49)(22,37,39,31)(25,41,42,46)(27,44,36,28)(30,38,48,34)(40,45,47,43);(15,17)(18,19)(20,29)(21,25)(22,27)(23,26)(24,32)(28,37)(30,47)(31,44)(33,46)(34,43)(35,42)(36,39)(38,45)(40,48)(41,49);(18,21,23,35)(19,25,26,42)(20,30,32,48)(22,38,39,34)(24,40,29,47)(27,45,36,43)(28,46,44,41)(31,49,37,33);(19,26)(24,29)(25,42)(27,36)(28,44)(40,47)(41,46)(43,45)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54074);