Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#10764 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | C4×C22⋊C4 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C8×C13 ◁ G | |
1194 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,28,30,24)(21,32,33,25)(22,27)(23,26)(29,36)(31,41,44,37)(34,45,46,38)(35,39)(40,43)(42,47)(48,49);(15,17)(18,20,22,31,23,30,35,44)(19,24,27,37,26,28,39,41)(21,29,34,42,33,43,46,49)(25,36,38,47,32,40,45,48);(18,21)(19,25)(20,29)(22,34)(23,33)(24,36)(26,32)(27,38)(28,40)(30,43)(31,42)(35,46)(37,47)(39,45)(41,48)(44,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3752);