Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C113 ⋊ #350 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22⋊D113 |
| commutator | C4×C113 | C2×C8 |
| Frattini | C2×C8 | C2×D113 |
| Fitting | #131×C113 | C2 |
| socle | C2×C113 | C22⋊C8 |
| hypercenter | #131 | D113 |
| hypocenter | C113 | #350 |
| LCS | G ▷ C4×C113 ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #131 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^112,c^b=cf,d^b=df1148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #350×D113, C2×#20298382, #28392200, … |
| maximal normal subgroup of | #350×D113, C2×#20298382, #28392200, … |
| maximal quotient of | #28388500, #28388516, D4⋊#14268622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 333);