Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#10625053 |
| Fitting | C2×C22⋊C4×C23 ⋊ C2 |
| Sylow | C23 ⋊ C2×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D23 |
| commutator, cosocle | C22×C23 | C24 |
| Frattini | C22 | C23×D23 |
| Fitting | C2×C22⋊C4×C23 | C2 |
| socle | C23×C23 | C23 |
| hypercenter | C2×C22⋊C4 | D23 |
| hypocenter | C23 | C2×#120 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
662 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 368 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | #15673804, #15673849, #15674522, … |
| maximal normal subgroup of | #15673804, #15673849, #15674522, … |
| maximal quotient of | C2×#13092272, C2×#13092291, C2×#13092292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1036);