Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C383 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D383 |
| commutator, socle | C2×C383 | C22×C4 |
| Fitting, prime radical | #41×C383 | C2 |
| cosocle | C4×C383 | C23 |
| hypercenter | #41 | D383 |
| hypocenter | C383 | #131 |
| LCS | G ▷ C2×C383 ▷ C383 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,383|a^2=d,d^2=e,f^a=f^382,c^b=ce1930 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37588465, #37588468, #37588470, … |
| maximal normal subgroup of | #37588465, #37588468, #37588470, … |
| maximal quotient of | #37588307, #37588318, #37588378, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 153);