Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C113 ⋊ C2 |
| Sylow | C113 ⋊ #519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D113 |
| commutator | C2×C113 | C23×C4 |
| Fitting | C4×Q8×C113 | C2 |
| socle | C22×C113 | C24 |
| hypercenter | C4×Q8 | D113 |
| hypocenter | C113 | #519 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
266 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=f,b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,g^d=g^1121154 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28399410, #28399412, #28399414, … |
| maximal normal subgroup of | #28399410, #28399412, #28399414, … |
| maximal quotient of | #28392928, #28392938, #28392939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1025);