Finite Group DatabasebetaFinite Group Databasebeta| order | 7136 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C223 ⋊ C2 |
| Sylow | C223 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D223 |
| commutator, socle | C22×C223 | C23 |
| Fitting | C42×C223 | C2 |
| hypercenter | C42 | D223 |
| hypocenter | C223 | #126 |
| LCS | G ▷ C22×C223 ▷ C223 | |
| UCS | C1 ◁ C22 ◁ C42 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,223|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^2221790 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D223, C2×#20297298, #28384113, … |
| maximal normal subgroup of | #126×D223, C2×#20297298, #28384113, … |
| maximal quotient of | #28383448, #28383464, #28383471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7136, 140);