Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#67290 |
| Fitting | C2×D4×C23 ⋊ C2 |
| Sylow | C23 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D23 |
| commutator, cosocle | C2×C23 | C24 |
| Frattini | C2 | C23×D23 |
| Fitting | C2×D4×C23 | C2 |
| socle | C22×C23 | C23 |
| hypercenter | C2×D4 | D23 |
| hypocenter | C23 | C2×#41 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 368 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #13092389, #13092398, #13092410, … |
| maximal normal subgroup of | #13092389, #13092398, #13092410, … |
| maximal quotient of | C2×#10625048, C2×#10625063, C2×(C22⋊D23)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 178);