Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| isoclinism | isoclinic class of #67272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#67272 |
| Fitting | C2×D4×C23 ⋊ C2 |
| Sylow | C23 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D23 |
| commutator, cosocle | C4×C23 | C23 |
| Frattini | C4 | C22×D23 |
| Fitting | C2×D4×C23 | C2 |
| socle | C22×C23 | D4 |
| hypercenter | C2×D4 | D23 |
| hypocenter | C23 | C2×D8 |
| LCS | G ▷ C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 368 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #13092497, C4×#67272, #13092526, … |
| maximal normal subgroup of | #13092497, C4×#67272, #13092526, … |
| maximal quotient of | C2×#10624991, C2×#10625014, C2×#10624989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 126);