Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12019 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#12887 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#106 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
286 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 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)(24,34,38,49)(25,40,39,53)(26,42)(27,43)(28,33)(29,37,47,50)(30,41,48,51)(31,36)(32,44)(35,46)(45,52);(15,18)(19,21)(22,24,35,50,27,39,52,41,28,38,26,37,44,25,36,51)(23,29,45,49,32,30,46,53,33,47,31,34,43,48,42,40);(14,16,17,20)(15,19,18,21)(22,25,26,41,27,24,36,37,28,39,35,51,44,38,52,50)(23,30,31,40,32,47,42,49,33,48,45,53,43,29,46,34)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5875);