Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C22⋊C4×C383 ⋊ C2 |
| Sylow | C383 ⋊ #124 |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,383|b^2=e,c^2=d,b^a=bd,c^a=ce,f^c=f^3821924 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #124×D383, C2×#27133827, #37588878, … |
| maximal normal subgroup of | #124×D383, C2×#27133827, #37588878, … |
| maximal quotient of | #37588215, #37588239, #37588240, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 132);