Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C113 ⋊ C8 |
| Sylow | C113 ⋊ #334 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C4⋊#11744762 |
| commutator | C4×C113 | C2×C8 |
| Frattini | C4 | C2×#11744762 |
| Fitting | C8×C113 | C8 |
| socle | C2×C113 | C4⋊C8 |
| hypercenter | C8 | #11744762 |
| hypocenter | C113 | #334 |
| LCS | G ▷ C4×C113 ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=c,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^18,g^d=g^98,g^f=g^112140 conjugacy classes — view the full character table.
| maximal subgroup of | #28407622, #28407623, #28407634, … |
| maximal normal subgroup of | #28407622, #28407623, #28407634, … |
| maximal quotient of | #28407580, #28407632, #28407633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1638);