Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#20297744 |
| derived, Sylow | C449 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #14267798 |
| commutator, hypocenter | C449 | C22×C8 |
| Frattini | C2 | C22×#14267798 |
| Fitting | C2×C4×C449 | C4 |
| socle | C22×C449 | C2×C4 |
| prime radical | C22×D449 | C4 |
| cosocle | Dic449 | C23 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7184 |
928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43272872, #43272880, #43272882, … |
| maximal normal subgroup of | #43272872, #43272880, #43272882, … |
| maximal quotient of | C2×C4×#16813318, C4×#20297744, #43272975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 229);