Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C113 ⋊ #334 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D452 |
| commutator | C4×C113 | C2×C8 |
| Frattini | C42 | C2×D113 |
| Fitting | C4×C8×C113 | C2 |
| socle | C22×C113 | C4⋊C4 |
| hypercenter | C4×C8 | D113 |
| hypocenter | C113 | #334 |
| LCS | G ▷ C4×C113 ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ C4×C8 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=c,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^1121820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28388541, #28388542, #28388544, … |
| maximal normal subgroup of | #28388541, #28388542, #28388544, … |
| maximal quotient of | #28388409, #28388638, #28388640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 300);