Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C113 ⋊ C2 |
| Sylow | C113 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D113 |
| commutator, socle | C2×C113 | C22×C8 |
| Fitting | M32×C113 | C2 |
| hypercenter | M32 | D113 |
| hypocenter | C113 | #504 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,d^2=e,e^2=f,g^a=g^112,c^b=cf,g^c=g^1121160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28392408, #28392410, #28392413, … |
| maximal normal subgroup of | #28392408, #28392410, #28392413, … |
| maximal quotient of | #28392172, #28392173, #28392186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 967);