Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C383 ⋊ C2 |
| Sylow | C383 ⋊ #99 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,383|a^2=d,b^a=bc,c^a=ce,d^b=de,f^b=f^3821921 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D383, C2×#27133755, #37588323, … |
| maximal normal subgroup of | #99×D383, C2×#27133755, #37588323, … |
| maximal quotient of | #37588074, #37588076, #37588084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 60);