Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D383)⋊C8 |
| Fitting | C2×C8×C383 ⋊ C2 |
| Sylow | C383 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,383|a^2=d,d^2=e,b^a=bc,f^b=f^3823076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C8×D383, C2×(C2×D383)⋊C8, #37588313, … |
| maximal normal subgroup of | C22⋊C8×D383, C2×(C2×D383)⋊C8, #37588313, … |
| maximal quotient of | #37588074, #37588076, #37588078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 58);