Finite Group DatabasebetaFinite Group Databasebeta| order | 7136 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q16×D223 |
| Fitting | Q16×C223 ⋊ C2 |
| Sylow | C223 ⋊ C2×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D223 |
| commutator | C4×C223 | C23 |
| Frattini | C4 | C22×D223 |
| Fitting | Q16×C223 | C2 |
| socle | C2×C223 | C2×D4 |
| hypercenter | Q16 | D223 |
| hypocenter | C223 | C2×Q16 |
| LCS | G ▷ C4×C223 ▷ C2×C223 ▷ C223 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
60 conjugacy classes of subgroups.
791 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D223, Q32×D223, #28384019, … |
| maximal normal subgroup of | SD32×D223, Q32×D223, #28384019, … |
| maximal quotient of | #103×D223, #107×D223, #28383672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7136, 162);