Finite Group DatabasebetaFinite Group Databasebeta| order | 7136 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C223 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D223 |
| commutator, socle | C22×C223 | C23 |
| Fitting | C22⋊C4×C223 | C2 |
| hypercenter | C22⋊C4 | D223 |
| hypocenter | C223 | C22⋊Q8 |
| LCS | G ▷ C22×C223 ▷ C223 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,223|a^2=d,b^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 | C22⋊Q8×D223, C2×#20297281, #28384086, … |
| maximal normal subgroup of | C22⋊Q8×D223, C2×#20297281, #28384086, … |
| maximal quotient of | #28383438, #28383452, #28383455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7136, 123);