Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10061 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,23,26)(20,27,29,32)(21,25,22,30)(24,31,33,28)(34,35,39,43)(36,44,47,48)(37,40,38,42)(41,45,49,46);(14,15)(16,17)(18,20,23,29)(19,24,26,33)(21,28,22,31)(25,32,30,27)(35,40)(37,38)(41,48)(42,43)(44,49)(45,46);(15,17)(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)(34,36,39,47)(35,41,43,49)(37,46,38,45)(40,48,42,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3049);