Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60454 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#60620 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#117 ◁ G | |
2014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23,28,33)(24,34,36,45)(25,39,40,47)(26,32,27,31)(29,38,44,37)(30,41,46,42)(35,43,49,53)(48,50,52,51);(15,18)(19,21)(22,24,27,38,28,36,26,37)(23,29,32,45,33,44,31,34)(25,35,42,51,40,49,41,50)(30,43,39,52,46,53,47,48);(14,16,17,20)(15,19,18,21)(22,25,26,41,28,40,27,42)(23,30,31,47,33,46,32,39)(24,35,37,50,36,49,38,51)(29,43,34,48,44,53,45,52);(25,40)(30,46)(35,49)(39,47)(41,42)(43,53)(48,52)(50,51);(24,36)(29,44)(34,45)(35,49)(37,38)(43,53)(48,52)(50,51)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53608);