Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #97×C113 ⋊ C2 |
| Sylow | C113 ⋊ #435 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D113 |
| commutator, socle | C22×C113 | C22×C4 |
| Fitting | #97×C113 | C2 |
| hypercenter | #97 | D113 |
| hypocenter | C113 | #435 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^112,g^b=g^1121148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #435×D113, C2×#20298671, #28399265, … |
| maximal normal subgroup of | #435×D113, C2×#20298671, #28399265, … |
| maximal quotient of | #28389405, #28389412, #28389419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 622);