Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C113 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D113 |
| commutator, socle | C2×C113 | C23×C4 |
| Fitting | C2×#41×C113 | C2 |
| hypercenter | C2×#41 | D113 |
| hypocenter | C113 | #568 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
258 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,e^2=f,d^a=df,g^a=g^112,c^b=cf1154 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28390793, #28390796, #28390812, … |
| maximal normal subgroup of | #28390793, #28390796, #28390812, … |
| maximal quotient of | #28398993, #28399002, #28399019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1316);