Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33662 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C22×C13 | C22×D8 |
| prime radical | C13×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
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)(16,19)(17,18)(20,21)(22,23)(24,28)(25,29)(26,39)(27,32)(30,36)(31,37)(33,40)(34,49)(35,43)(38,45)(41,46)(42,47)(44,50)(48,52)(51,53);(15,18)(19,21)(22,24,27,35)(23,28,32,43)(25,33,38,48)(26,34,37,47)(29,40,45,52)(30,41,44,51)(31,42,39,49)(36,46,50,53);(23,29)(25,36)(26,37)(28,40)(30,31)(32,45)(33,46)(34,47)(38,50)(39,44)(41,42)(43,52)(48,53)(49,51);(14,16,17,20)(15,19,18,21)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26650);