Finite Group DatabasebetaFinite Group Databasebeta| order | 7164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×C3×C199⋊C3 |
| Fitting, socle | C22×C3×C199 ⋊ C3 |
| derived, Sylow | C199 ⋊ C22×C32 |
| Hall | C22×C199 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | C199⋊C3 |
| commutator, hypocenter | C199 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C199 | C3 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C22×C3 | |
60 conjugacy classes of subgroups.
828 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×D5×C199⋊C3, C22×C3×C5×C199⋊C3 |
| maximal normal subgroup of | C22×C3×C5×C199⋊C3 |
| maximal quotient of | C2×C3×D5×C199⋊C3, C22×C3×C5×C199⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7164, 46);