Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C383 ⋊ #125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D383 |
| commutator, socle, prime radical, cosocle | C22×C383 | C23 |
| Fitting | C4⋊C4×C383 | C2 |
| hypercenter | C4⋊C4 | D383 |
| hypocenter | C383 | #125 |
| LCS | G ▷ C22×C383 ▷ C383 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,383|a^2=d,b^2=e,c^2=d,b^a=bd,c^a=ce,f^b=f^382,f^c=f^3821924 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37588649, #37588650, #37588653, … |
| maximal normal subgroup of | #37588649, #37588650, #37588653, … |
| maximal quotient of | #37588216, #37588234, #37588238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 137);