Finite Group DatabasebetaFinite Group Databasebeta| order | 12128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D8×C379 ⋊ C2 |
| Sylow | C379 ⋊ AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D379 |
| commutator, cosocle | C4×C379 | C23 |
| Frattini | C4 | C22×D379 |
| Fitting | D8×C379 | C2 |
| socle | C2×C379 | C2×D4 |
| hypercenter | D8 | D379 |
| hypocenter | C379 | AGL(1,ℤ/8) |
| LCS | G ▷ C4×C379 ▷ C2×C379 ▷ C379 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,379|d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^c=f^3781334 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/8)×D379, C2×#27131355, #37566040, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D379, C2×#27131355, #37566040, … |
| maximal quotient of | #37565242, #37565247, #37565285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12128, 170);