Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C113 ⋊ C2 |
| Sylow | C113 ⋊ #518 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D113 |
| commutator | C2×C113 | C23×C4 |
| Fitting | C2×C22⋊C4×C113 | C2 |
| socle | C22×C113 | C24 |
| hypercenter | C2×C22⋊C4 | D113 |
| hypocenter | C113 | #518 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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,c^b=ce,g^c=g^1121154 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28390681, #28390853, #28390856, … |
| maximal normal subgroup of | #28390681, #28390853, #28390856, … |
| maximal quotient of | #28392926, #28392927, #28392929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1022);