Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C233 ⋊ C2 |
| Sylow | C233 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D233 |
| commutator, socle | C22×C233 | C23 |
| Fitting | C4⋊C4×C233 | C2 |
| hypercenter | C4⋊C4 | D233 |
| hypocenter | C233 | #123 |
| LCS | G ▷ C22×C233 ▷ C233 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|c^2=d,b^a=bd,c^a=ce,f^a=f^232,f^b=f^2321174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #123×D233, C2×#21418520, #28416944, … |
| maximal normal subgroup of | #123×D233, C2×#21418520, #28416944, … |
| maximal quotient of | #28416297, #28416306, #28416313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 131);