Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C113 ⋊ C4 |
| Sylow | C113 ⋊ #518 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#90673 |
| commutator, socle | C2×C113 | C23×C4 |
| Fitting | C2×D4×C113 | C4 |
| hypercenter | C2×D4 | #90673 |
| hypocenter | C113 | #518 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
338 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,113|a^2=f,b^a=be,d^a=de,g^a=g^98,c^b=ce,g^f=g^112314 conjugacy classes — view the full character table.
| maximal subgroup of | #28406529, #28406545, #28406579, … |
| maximal normal subgroup of | #28406529, #28406545, #28406579, … |
| maximal quotient of | #28407010, #28407012, #28407013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1616);