Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×D113 |
| Fitting | C22×Q8×C113 ⋊ C2 |
| Sylow | C113 ⋊ C23×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D113 |
| commutator | C2×C113 | C25 |
| Frattini | C2 | C24×D113 |
| Fitting | C22×Q8×C113 | C2 |
| socle | C23×C113 | C23 |
| hypercenter | C22×Q8 | D113 |
| hypocenter | C113 | C23×Q8 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
850 conjugacy classes of subgroups.
1160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28390496, #28390507, #391×D113, … |
| maximal normal subgroup of | #28390496, #28390507, #391×D113, … |
| maximal quotient of | C22×C4⋊C4×D113, C2×C4×Q8×D113, C22×#16813587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1372);