Finite Group DatabasebetaFinite Group Databasebeta| order | 12256 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C383 ⋊ C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D383 |
| commutator, socle, prime radical, cosocle | C22×C383 | C23 |
| Fitting | C2×Q8×C383 | C2 |
| hypercenter | C2×Q8 | D383 |
| hypocenter | C383 | C4⋊Q8 |
| LCS | G ▷ C22×C383 ▷ C383 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,383|a^2=d,b^2=d,c^2=e,b^a=bd,c^a=ce,f^c=f^3821924 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37588149, #37588532, #37588534, … |
| maximal normal subgroup of | #37588149, #37588532, #37588534, … |
| maximal quotient of | #37588220, #37588246, #37588256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12256, 144);