Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | D4×Q8×C173 ⋊ C2 |
| Sylow | C173 ⋊ #3486 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D173 |
| commutator, socle, cosocle | C22×C173 | C25 |
| Fitting | D4×Q8×C173 | C2 |
| hypercenter | D4×Q8 | D173 |
| hypocenter | C173 | #3486 |
| LCS | G ▷ C22×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|b^2=f,d^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^172,h^e=h^1722194 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 18160);