Finite Group DatabasebetaFinite Group Databasebeta| order | 546 |
| isoclinism | isoclinic class of #10587716 |
| 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 | C7×D13 ⋊ C3 |
| Hall | D13 ⋊ ΓL(1,𝔽8) |
| Sylow | C13 ⋊ C2×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ D13⋊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|d^a=d^12,c^b=c^2,d^b=d^324 conjugacy classes — view the full character table.
| maximal subgroup of | #11763982, #11763985, #10587716⋊C2, … |
| maximal normal subgroup of | #11763982, #11763985, #10587716⋊C2, … |
| maximal quotient of | #11763957, C2×#10587716, #13109896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(546, 5);