Finite Group DatabasebetaFinite Group Databasebeta| order | 6111 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C97 ⋊ C9 |
| Sylow | C97 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ C97⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #14523271 |
| commutator, hypocenter | C7×C97 | C9 |
| Fitting, socle | C3×C7×C97 | C3 |
| LCS | G ▷ C7×C97 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,97,3|a^3=d,b^a=b^2,c^a=c^35687 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20259169, #27132056, #27132060, … |
| maximal normal subgroup of | C2×#20259169, #27132056, #27132060, … |
| maximal quotient of | C2×#20259169, C22⋊#20259169, C5×#20259169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6111, 4);