Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23440 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1898 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)(20,30)(21,35)(22,29)(23,28)(24,27)(25,32)(26,37)(31,46)(33,41)(34,42)(36,43)(38,44)(39,45)(40,48)(47,49);(15,17)(18,20)(19,25)(21,36)(22,33)(23,32)(24,34)(26,43)(27,41)(28,42)(29,30)(31,38)(35,46)(37,48)(39,47)(40,45)(44,49);(18,21,24,39)(19,26,27,44)(20,31,34,48)(22,38,23,37)(25,40,41,46)(28,45,29,35)(30,43,42,49)(32,36,33,47);(19,27)(25,41)(26,44)(28,29)(30,42)(35,45)(40,46)(43,49)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16428);