Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C113 ⋊ C4 |
| Sylow | C113 ⋊ #347 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×#90673 |
| commutator | C4×C113 | C42 |
| Frattini | C8 | C2×#90673 |
| Fitting | C16×C113 | C4 |
| socle | C2×C113 | #97 |
| hypercenter | C16 | #90673 |
| hypocenter | C113 | #347 |
| LCS | G ▷ C4×C113 ▷ C113 | |
| UCS | C1 ◁ C4 ◁ C16 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,c^b=cf,g^b=g^98,g^d=g^112470 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20299488, #28406789, #28406793, … |
| maximal normal subgroup of | C2×#20299488, #28406789, #28406793, … |
| maximal quotient of | #28405490, #28405493, #28405614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1439);