Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12946 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19,23,29)(20,31,34,47)(21,25,39,28)(22,40,36,27)(24,41,38,30)(26,37,45,33)(32,46,49,48)(35,44,42,43);(14,16,17,15)(19,25)(21,36)(22,39)(24,38)(26,43)(27,30)(28,29)(31,46)(32,33)(35,42)(37,49)(40,41)(44,45)(47,48);(18,20)(19,26)(21,37)(22,32)(23,34)(24,42)(25,43)(27,47)(28,44)(29,45)(30,48)(31,40)(33,39)(35,38)(36,49)(41,46)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5934);