Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C113 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #90673 |
| commutator, hypocenter | C113 | C2×C32 |
| Frattini | C8 | C2×#90673 |
| Fitting | C16×C113 | C4 |
| socle | C2×C113 | C2×C16 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C16 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^98,g^b=g^112,g^c=g^112512 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#90673, #28405680, #28405723, … |
| maximal normal subgroup of | C32×#90673, #28405680, #28405723, … |
| maximal quotient of | #28405679, #28405688, #28405732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1480);