Finite Group DatabasebetaFinite Group Databasebeta| order | 18016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D8×C563 ⋊ C2 |
| Sylow | C563 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D563 |
| commutator, cosocle | C4×C563 | C23 |
| Frattini | C4 | C22×D563 |
| Fitting | D8×C563 | C2 |
| socle | C2×C563 | C2×D4 |
| hypercenter | D8 | D563 |
| hypocenter | C563 | #135 |
| LCS | G ▷ C4×C563 ▷ C2×C563 ▷ C563 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9008 |
Polycyclic presentation:
2^5,563|c^2=e,d^2=e,b^a=bd,d^a=de,d^b=de,f^c=f^5621981 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49113917, #49113919, #49113922, … |
| maximal normal subgroup of | #49113917, #49113919, #49113922, … |
| maximal quotient of | #49113481, #49113525, D8×Dic563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18016, 165);