Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C113 ⋊ #346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#11744762 |
| commutator | C2×C113 | C4×C8 |
| Fitting | C2×C4×C113 | C8 |
| socle | C22×C113 | C2×C8 |
| hypercenter | C2×C4 | #11744762 |
| hypocenter | C113 | #346 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^a=g^18,g^c=g^98,g^e=g^112152 conjugacy classes — view the full character table.
| maximal subgroup of | #28407618, #28407619, #28407630, … |
| maximal normal subgroup of | #28407618, #28407619, #28407630, … |
| maximal quotient of | #28407590, #28407592, #28407644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1643);