Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| isoclinism | isoclinic class of #67263 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D184 |
| Fitting | C22×C8×C23 ⋊ C2 |
| Sylow | C23 ⋊ C22×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D92 |
| commutator, cosocle | C4×C23 | C24 |
| Frattini | C4 | C23×D23 |
| Fitting | C22×C8×C23 | C2 |
| socle | C23×C23 | D4 |
| hypercenter | C22×C8 | D23 |
| hypocenter | C23 | C22×D8 |
| LCS | G ▷ C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
380 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15673744, #15673746, #15674261, … |
| maximal normal subgroup of | #15673744, #15673746, #15674261, … |
| maximal quotient of | C22×#10625003, C22×#10625000, C2×C4×D184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1319);