Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #447×C167 ⋊ C2 |
| Sylow | C167 ⋊ #3297 |
420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5344 |
Polycyclic presentation:
2^7,167|a^2=eg,b^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^166,d^b=de,h^b=h^166,f^c=fg1612 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 16364);