Finite Group DatabasebetaFinite Group Databasebeta| order | 7136 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C223 ⋊ C2 |
| Sylow | C223 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D223 |
| commutator, socle | C22×C223 | C23 |
| Fitting | C22⋊C4×C223 | C2 |
| hypercenter | C22⋊C4 | D223 |
| hypocenter | C223 | #123 |
| LCS | G ▷ C22×C223 ▷ C223 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,223|c^2=d,b^a=bd,c^a=ce,f^b=f^2221124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #123×D223, C2×#20297286, #28384089, … |
| maximal normal subgroup of | #123×D223, C2×#20297286, #28384089, … |
| maximal quotient of | #28383442, #28383454, #28383456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7136, 128);