Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C383 ⋊ #117 |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,383|a^2=e,c^2=d,b^a=bd,f^a=f^3823076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37588107, #37588108, #37588111, … |
| maximal normal subgroup of | #37588107, #37588108, #37588111, … |
| maximal quotient of | #37588197, C4×C22⋊Dic383, C4×C4⋊Dic383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 105);