Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×#124×C181 ⋊ C2 |
| Sylow | C181 ⋊ #3510 |
1040 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
Polycyclic presentation:
2^7,181|b^2=g,c^2=fg,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^1802564 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 18404);