Finite Group DatabasebetaFinite Group Databasebeta| order | 14864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#21418261 |
| Fitting, socle | C2×C929 ⋊ C8 |
| derived, Sylow | C929 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #21418261 |
| commutator, hypocenter | C929 | C2×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C929 | C8 |
| prime radical | C2×D929 | C4 |
| cosocle | #16836500 | C22 |
| LCS | G ▷ C929 | |
| UCS | C1 ◁ C2 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1858 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#21418261, C22⋊#21418261, C4⋊#21418261, … |
| maximal normal subgroup of | C4×#21418261, C22⋊#21418261, C4⋊#21418261, … |
| maximal quotient of | C4×#21418261, C22⋊#21418261, C4⋊#21418261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14864, 53);