Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×#14267798 |
| Fitting | C8×C449 ⋊ C4 |
| derived, Sylow | C449 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #14267798 |
| commutator, hypocenter | C449 | C4×C8 |
| Frattini | C4 | C2×#14267798 |
| Fitting | C8×C449 | C4 |
| socle | C2×C449 | C42 |
| prime radical | C2×D449 | C2×C4 |
| cosocle | C4×D449 | C22 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3592 |
928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#14267798, #43272894, C2×C8×#14267798, … |
| maximal normal subgroup of | C16×#14267798, #43272894, C2×C8×#14267798, … |
| maximal quotient of | C8×#16813318, #43272849, #43272872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 198);