Finite Group DatabasebetaFinite Group Databasebeta| order | 273 |
| isoclinism | isoclinic class of #63270 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C13 ⋊ C3 |
| Sylow | C13 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 91 |
A minimal faithful permutation representation — 2 generators on 20 points:
(2,3,5)(4,7,10)(6,9,8)(11,13,12)(15,16,17)(18,20,19);(1,2,4,3,6,10,7,11,13,5,8,12,9)(14,15,16,18,17,19,20)Polycyclic presentation:
3,7,13|b^a=b^2,c^a=c^333 conjugacy classes — view the full character table.
| maximal subgroup of | #10587716, #10587720, #10587722, … |
| maximal normal subgroup of | #10587716, #10587720, #10587722, … |
| maximal quotient of | C2×#63270, #11717941, C3×#63270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(273, 3);