Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
706 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,20)(16,19,17,21)(22,23)(24,35)(25,30)(26,43)(27,33)(28,34)(29,38)(31,42)(32,45)(36,49)(37,46)(39,47)(40,53)(41,50)(44,48)(51,52);(14,16,18,17)(15,19,20,21)(22,24)(23,29)(25,40)(26,37)(27,44)(28,39)(30,49)(31,46)(32,47)(33,35)(34,48)(36,42)(38,45)(41,52)(43,51)(50,53);(14,17,18,16)(15,19,20,21)(22,25,28,26)(23,30,34,43)(24,36,39,52)(27,41,45,42)(29,46,48,53)(31,33,50,32)(35,49,47,51)(37,44,40,38);(22,26,28,25)(23,31,34,50)(24,37,39,40)(27,41,45,42)(29,46,48,53)(30,33,43,32)(35,51,47,49)(36,44,52,38)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19391);