Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C233 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14272347 |
| commutator, socle | C2×C233 | C2×C8 |
| Fitting | C4×C233 | C8 |
| hypercenter | C4 | #14272347 |
| hypocenter | C233 | M32 |
| LCS | G ▷ C2×C233 ▷ C233 | |
| UCS | C1 ◁ C2 ◁ C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^221,f^b=f^232,f^c=f^144,f^d=f^232136 conjugacy classes — view the full character table.
| maximal subgroup of | #28417535, #28417536, #28417539, … |
| maximal normal subgroup of | #28417535, #28417536, #28417539, … |
| maximal quotient of | #28417529, #28417532, C4⋊#16836606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 243);