Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D233⋊M16 |
| Sylow | C233 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×#11745400 |
| commutator, socle | C2×C233 | C22×C4 |
| Frattini | C2 | C22×#11745400 |
| Fitting | C2×C4×C233 | C4 |
| hypercenter | C2×C4 | #11745400 |
| hypocenter | C233 | C2×M16 |
| LCS | G ▷ C2×C233 ▷ C233 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|a^2=d,d^2=e,b^a=be,f^a=f^144,f^c=f^232,f^d=f^232484 conjugacy classes — view the full character table.
| maximal subgroup of | #28417302, #28417304, #28417306, … |
| maximal normal subgroup of | #28417302, #28417304, #28417306, … |
| maximal quotient of | #28417394, C4×#16836603, C4×#16836604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 231);