Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C383 ⋊ #97 |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,383|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^3823076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37588128, #97×D383, C2×#27133751, … |
| maximal normal subgroup of | #37588128, #97×D383, C2×#27133751, … |
| maximal quotient of | #37588072, #37588073, #37588105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 56);