Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C8×D23 |
| Fitting | C4×C8×C23 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D23 |
| commutator, hypocenter | C23 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D23 |
| Fitting | C4×C8×C23 | C2 |
| socle | C22×C23 | C22×C4 |
| prime radical | C22×D23 | C2×C4 |
| cosocle | C2×C4×C23 | C23 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C4×C8 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C82×D23, D23×#322, C8×#67262, … |
| maximal normal subgroup of | C82×D23, D23×#322, C8×#67262, … |
| maximal quotient of | C82×D23, D23×#322, C8×#67262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 493);