Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#16836606 |
| derived, Sylow | C233 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #14272347 |
| commutator, hypocenter | C233 | C2×C16 |
| Frattini | C2 | C2×#14272347 |
| Fitting, socle | C22×C233 | C8 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C22 | |
28 conjugacy classes of subgroups.
148 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16836606, #28417529, C22⋊#16836606, … |
| maximal normal subgroup of | C4×#16836606, #28417529, C22⋊#16836606, … |
| maximal quotient of | C4×#16836606, C22⋊#16836606, C4⋊#16836606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 240);