Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#10625111 |
| Fitting | C22×D4×C23 ⋊ C2 |
| Sylow | C23 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D23 |
| commutator, cosocle | C22×C23 | C24 |
| Frattini | C22 | C23×D23 |
| Fitting | C22×D4×C23 | C2 |
| socle | C23×C23 | C23 |
| hypercenter | C22×D4 | D23 |
| hypocenter | C23 | C2×#127 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | #15673792, #15673793, #15673795, … |
| maximal normal subgroup of | #15673792, #15673793, #15673795, … |
| maximal quotient of | C2×#13092286, C2×#13092317, C2×#13092318, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1088);