Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| isoclinism | isoclinic class of Dic46 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#67288 |
| Fitting | C22×C4×C23 ⋊ C2 |
| Sylow | C23 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D23 |
| commutator, cosocle | C2×C23 | C24 |
| Frattini | C2 | C23×D23 |
| Fitting | C22×C4×C23 | C2 |
| socle | C22×C23 | C23 |
| hypercenter | C22×C4 | D23 |
| hypocenter | C23 | C2×#41 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 368 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | #13092382, #13092383, #13092385, … |
| maximal normal subgroup of | #13092382, #13092383, #13092385, … |
| maximal quotient of | C2×#10625043, C2×#10625097, C2×C4×C22⋊D23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 176);