Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #557×C167 ⋊ C2 |
| Sylow | C167 ⋊ Q8×#41 |
1068 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10688 |
Polycyclic presentation:
2^7,167|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,h^b=h^166,h^d=h^166,h^e=h^1662125 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 18092);