Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23444 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| prime radical | C13×#3449 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,24)(21,25)(22,26)(23,27)(28,35)(29,36)(30,37)(31,39)(32,40)(33,41)(34,42)(38,44)(43,47)(45,48)(46,49);(18,20,23,30)(19,24,27,37)(21,28,32,44)(22,33,34,29)(25,38,40,35)(26,41,42,36)(31,45,46,43)(39,47,49,48);(15,17)(18,21)(19,25)(20,28)(22,31)(23,32)(24,35)(26,39)(27,40)(29,43)(30,44)(33,45)(34,46)(36,47)(37,38)(41,48)(42,49);(18,22,23,34)(19,26,27,42)(20,29,30,33)(21,31,32,46)(24,36,37,41)(25,39,40,49)(28,43,44,45)(35,47,38,48)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16434);