Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #344 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14268624 |
| commutator | C22×C113 | C42 |
| Frattini | C22×C4 | C2×D113 |
| Fitting | #117×C113 | C2 |
| socle | C2×C113 | #95 |
| hypercenter | #117 | D113 |
| hypocenter | C113 | #344 |
| LCS | G ▷ C22×C113 ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #117 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,e^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^1121142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #344×D113, C2×#20298368, #28390375, … |
| maximal normal subgroup of | #344×D113, C2×#20298368, #28390375, … |
| maximal quotient of | #28388418, #28388422, #28388423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 319);