Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C113 ⋊ #491 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D452 |
| commutator | C2×C4×C113 | C23 |
| Frattini | C2×C4 | C22×D113 |
| Fitting | #97×C113 | C2 |
| socle | C22×C113 | C2×D4 |
| hypercenter | #97 | D113 |
| hypocenter | C113 | #491 |
| LCS | G ▷ C2×C4×C113 ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=f,b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^112,c^b=cf1136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28388608, #28389899, #28389904, … |
| maximal normal subgroup of | #28388608, #28389899, #28389904, … |
| maximal quotient of | #28390708, #28391264, #28391394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 918);