Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33527 |
| 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 | |
1098 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)(22,35)(23,33)(24,28)(25,31)(27,37)(30,46)(32,47)(34,44)(36,40)(38,45)(39,43)(41,49)(42,48);(18,20,24,32)(19,25,28,42)(21,30,23,39)(22,36,38,49)(26,40,33,41)(27,43,44,46)(29,45,47,35)(31,34,48,37);(15,17)(18,19)(20,25)(21,33)(22,27)(23,26)(24,28)(29,31)(30,41)(32,42)(34,45)(35,37)(36,43)(38,44)(39,40)(46,49)(47,48);(18,21,24,23)(19,26,28,33)(20,30,32,39)(22,34,38,37)(25,40,42,41)(27,35,44,45)(29,46,47,43)(31,36,48,49)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26515);