Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#10842 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C2×D4 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ C22×C42×C13 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(19,21)(22,23,24,25)(26,27)(28,36)(29,35)(30,33)(31,34)(32,37)(38,41)(39,40);(15,17)(26,28,31,39,30,38,29,37)(27,32,35,41,33,40,34,36);(18,19,20,21)(27,33)(32,40)(34,35)(36,41)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3830);