Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C42×C113 ⋊ C4 |
| Sylow | C113 ⋊ #376 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#90673 |
| commutator | C2×C113 | C2×C42 |
| Frattini | C22 | C22×#90673 |
| Fitting | C42×C113 | C4 |
| socle | C22×C113 | C22×C4 |
| hypercenter | C42 | #90673 |
| hypocenter | C113 | #376 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
178 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,b^2=f,c^2=d,b^a=bd,g^a=g^98,g^e=g^112488 conjugacy classes — view the full character table.
| maximal subgroup of | #28405397, #28405461, #28405463, … |
| maximal normal subgroup of | #28405397, #28405461, #28405463, … |
| maximal quotient of | C4×(C2×#90673)⋊C4, #28405749, #28405750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1485);