Finite Group DatabasebetaFinite Group Databasebeta| order | 4802 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C73 · Schur multiplier (H2) = C74 |
| direct product | C2×C7×H(3,𝔽7) |
| unambiguous semidirect product | (C2×C72)⋊C72 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C72 | C72 |
| commutator, Frattini, cosocle | C7 | C2×C73 |
| LCS | G ▷ C7 ▷ C1 | |
| UCS | C1 ◁ C2×C72 ◁ G | |
472 conjugacy classes of subgroups.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 686 |
A minimal faithful permutation representation — 3 generators on 58 points:
(1,2)(3,4,5,6,7,8,9);(10,11,13,17,24,35,44)(12,15,19,26,37,46,53)(14,20,30,42,51,58,52)(16,22,29,39,48,45,54)(18,27,40,50,57,43,21)(23,33,28,41,36,47,55)(25,38,49,56,34,32,31);(11,14,21,32,33,22,15)(13,18,28,19,20,31,29)(17,25,26,27,39,30,41)(24,36,42,48,40,37,38)(35,45,49,51,46,47,50)(44,53,54,55,56,57,58)770 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4802, 12);