Finite Group DatabasebetaFinite Group Databasebeta| order | 12128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C379 ⋊ C2 |
| Sylow | C379 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D379 |
| commutator, socle, cosocle | C22×C379 | C23 |
| Fitting | C4⋊C4×C379 | C2 |
| prime radical | C2×D1516 | C2 |
| hypercenter | C4⋊C4 | D379 |
| hypocenter | C379 | #123 |
| LCS | G ▷ C22×C379 ▷ C379 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,379|c^2=d,b^a=bd,c^a=ce,f^a=f^378,f^b=f^3781904 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #123×D379, C2×#27131316, #37565753, … |
| maximal normal subgroup of | #123×D379, C2×#27131316, #37565753, … |
| maximal quotient of | #37565106, #37565115, #37565122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12128, 131);