Finite Group DatabasebetaFinite Group Databasebeta| order | 546 |
| isoclinism | isoclinic class of #10587720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C13 ⋊ C2×C3 |
| Hall | #63270 ⋊ C2 |
| Hall | C13×D7 ⋊ C3 |
| Hall | D7 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ AGL(1,𝔽7) |
| Sylow | C7 ⋊ C2×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13 | C2×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 91 |
Polycyclic presentation:
2,3,7,13|c^a=c^6,c^b=c^2,d^b=d^327 conjugacy classes — view the full character table.
| maximal subgroup of | #10587716⋊C2, C2×#10587720, C13⋊C3×AGL(1,𝔽7), … |
| maximal normal subgroup of | #10587716⋊C2, C2×#10587720, C13⋊C3×AGL(1,𝔽7), … |
| maximal quotient of | #11763961, C2×#10587720, #13109900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(546, 9);