Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C113 ⋊ #336 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C2×D113 |
| commutator | C2×C113 | C4×C8 |
| Fitting | C2×C42×C113 | C2 |
| socle | C23×C113 | C2×C4 |
| hypercenter | C2×C42 | D113 |
| hypocenter | C113 | #336 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,d^2=f,b^a=bc,g^a=g^1121832 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28388394, #28388395, #28388396, … |
| maximal normal subgroup of | #28388394, #28388395, #28388396, … |
| maximal quotient of | #28388401, #28388403, #28388405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 304);