Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26851 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
720 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)(16,21)(17,19)(18,20)(22,23)(24,36)(25,42)(26,46)(27,34)(28,33)(29,35)(30,39)(31,44)(32,37)(38,52)(40,49)(41,48)(43,50)(45,51)(47,53);(14,16,18,17)(15,19,20,21)(22,24,28,40,29,41,27,39)(23,30,34,48,35,49,33,36)(25,43,44,37,45,26,38,47)(31,50,42,53,52,46,51,32);(14,17,18,16)(15,19,20,21)(22,25,27,38,29,45,28,44)(23,31,33,51,35,52,34,42)(24,37,39,43,41,47,40,26)(30,32,36,46,49,53,48,50);(15,20)(19,21)(22,26,27,37,29,43,28,47)(23,32,33,46,35,53,34,50)(24,38,39,45,41,44,40,25)(30,31,36,51,49,52,48,42)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19839);