Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13385 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3061 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
408 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)(15,16)(18,19)(20,30)(21,26)(22,25)(23,28)(24,32)(27,37)(29,36)(31,39)(33,47)(34,43)(35,41)(38,48)(40,46)(42,49)(44,45);(14,15)(16,17)(18,20)(19,24)(21,32)(22,33)(23,31)(25,40)(26,30)(27,38)(28,43)(29,39)(34,36)(35,46)(37,45)(41,47)(42,44)(48,49);(14,16,17,15)(19,25)(20,31)(22,37)(23,36)(24,38)(26,41)(27,29)(28,42)(30,44)(32,34)(33,46)(35,49)(39,47)(40,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6373);