Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×#14267798 |
| Fitting | Q8×C449 ⋊ C4 |
| Sylow | C449 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#14267798 |
| commutator, socle | C2×C449 | C22×C4 |
| Fitting | Q8×C449 | C4 |
| prime radical, cosocle | C2×D449 | C23 |
| hypercenter | Q8 | #14267798 |
| hypocenter | C449 | C4×Q8 |
| LCS | G ▷ C2×C449 ▷ C449 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3592 |
580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×#14267798, Q16×#14267798, #43273046, … |
| maximal normal subgroup of | SD16×#14267798, Q16×#14267798, #43273046, … |
| maximal quotient of | C4⋊C4×#14267798, #43272956, #43272958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 227);