Finite Group DatabasebetaFinite Group Databasebeta| order | 14752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D461⋊C8 |
| unambiguous semidirect product | D461⋊(C2×C8) |
| derived, Sylow | C461 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #14270406 |
| commutator, hypocenter | C461 | C22×C8 |
| Frattini | C2 | C22×#14270406 |
| Fitting | C2×C4×C461 | C4 |
| socle | C22×C461 | C2×C4 |
| prime radical | C22×D461 | C4 |
| cosocle | Dic461 | C23 |
| LCS | G ▷ C461 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7376 |
952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×#14270406)⋊C8, #44442949, #44442951, … |
| maximal normal subgroup of | (C2×#14270406)⋊C8, #44442949, #44442951, … |
| maximal quotient of | C2×C4×#16814786, C4×D461⋊C8, D461⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14752, 229);