Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#10625158 |
| Fitting | C22×Q8×C23 ⋊ C2 |
| Sylow | C23 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D23 |
| commutator, cosocle | C2×C23 | C25 |
| Frattini | C2 | C24×D23 |
| Fitting | C22×Q8×C23 | C2 |
| socle | C22×C23 | C24 |
| hypercenter | C22×Q8 | D23 |
| hypocenter | C23 | C2×2−1+4 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
254 conjugacy classes — view the full character table.
| maximal subgroup of | #15673355, #15673358, #15673369, … |
| maximal normal subgroup of | #15673355, #15673358, #15673369, … |
| maximal quotient of | C2×#13092893, C2×#13092895, C2×#13092898, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1383);