Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D8×D23 |
| Fitting | C2×D8×C23 ⋊ C2 |
| Sylow | C23 ⋊ C22×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D23 |
| commutator, cosocle | C4×C23 | C24 |
| Frattini | C4 | C23×D23 |
| Fitting | C2×D8×C23 | C2 |
| socle | C22×C23 | C2×D4 |
| hypercenter | C2×D8 | D23 |
| hypocenter | C23 | C22×D8 |
| LCS | G ▷ C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D8 | |
338 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 368 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#357, #15675111, D23×#361, … |
| maximal normal subgroup of | D23×#357, #15675111, D23×#361, … |
| maximal quotient of | C2×#102×D23, C2×#107×D23, C4×D8×D23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1317);