Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D113⋊#131 |
| Sylow | C113 ⋊ C2×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#90673 |
| commutator, socle | C2×C113 | C23×C4 |
| Frattini | C2 | C23×#90673 |
| Fitting | #41×C113 | C4 |
| hypercenter | #41 | #90673 |
| hypocenter | C113 | C2×#131 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C4 ◁ #41 | |
266 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,e^2=f,g^a=g^98,c^b=cf,g^d=g^112,g^e=g^112320 conjugacy classes — view the full character table.
| maximal subgroup of | #28406350, #28406354, #28406613, … |
| maximal normal subgroup of | #28406350, #28406354, #28406613, … |
| maximal quotient of | #28407134, C4×#16813709, C4×#16813710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1625);