Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | 2−1+4×D23 |
| Fitting | C23×2−1+4 ⋊ C2 |
| Sylow | C23 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D23 |
| commutator, socle, cosocle | C2×C23 | C25 |
| Fitting | C23×2−1+4 | C2 |
| hypercenter | 2−1+4 | D23 |
| hypocenter | C23 | C2×2−1+4 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 368 |
221 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#454, D23×#456, #15682758, … |
| maximal normal subgroup of | D23×#454, D23×#456, #15682758, … |
| maximal quotient of | D23×#519, D23×#520, #15686606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1381);