Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33610 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,29)(21,26)(22,37)(23,35)(24,28)(25,32)(27,30)(31,42)(33,48)(34,44)(36,41)(38,49)(39,46)(40,47)(43,45);(18,20,30,45,23,33,38,47,24,34,36,46,21,31,22,32)(19,25,37,42,26,39,41,44,28,40,49,48,35,43,27,29);(15,17)(18,19)(20,25)(21,35)(22,27)(23,26)(24,28)(29,32)(30,37)(31,43)(33,39)(34,40)(36,49)(38,41)(42,45)(44,47)(46,48);(18,21,24,23)(19,26,28,35)(20,31,34,33)(22,36,38,30)(25,39,40,43)(27,37,41,49)(29,42,44,48)(32,46,47,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26598);