Finite Group DatabasebetaFinite Group Databasebeta| order | 5652 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle | C2×C3×C157 ⋊ C2×C3 |
| derived, Sylow | C157 ⋊ C22×C32 |
| Hall | C3×C157⋊C3 ⋊ C22 |
| Hall | C2×D157 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D157⋊C3 |
| commutator, hypocenter | C157 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C157 | C2×C3 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C2×C3 | |
60 conjugacy classes of subgroups.
192 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×D157⋊C3, C2×C3×C5×D157⋊C3, C2×C3×C5⋊(D157⋊C3) |
| maximal normal subgroup of | C2×C3×C5×D157⋊C3 |
| maximal quotient of | C3×D5×D157⋊C3, C2×C3×C5×D157⋊C3, C2×C3×C5⋊(D157⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5652, 34);