Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C383 ⋊ C22⋊Q8 |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,383|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^3821924 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊Q8×D383, C2×#27133818, #37588857, … |
| maximal normal subgroup of | C22⋊Q8×D383, C2×#27133818, #37588857, … |
| maximal quotient of | #37588209, #37588223, #37588226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 123);