Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #95×C113 ⋊ C2 |
| Sylow | C113 ⋊ C4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D113 |
| commutator | C2×C113 | C2×C42 |
| Fitting | #95×C113 | C2 |
| socle | C23×C113 | C23 |
| hypercenter | #95 | D113 |
| hypocenter | C113 | C4×C22⋊C4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ #95 | |
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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=e,b^2=f,c^2=e,b^a=bd,g^c=g^1121160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28389062, #28389064, #28389088, … |
| maximal normal subgroup of | #28389062, #28389064, #28389088, … |
| maximal quotient of | #95×Dic113, #28388795, #28388800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 396);