Finite Group DatabasebetaFinite Group Databasebeta| order | 12128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q8×C379 ⋊ C2 |
| Sylow | C379 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D379 |
| commutator, socle, cosocle | C22×C379 | C23 |
| Fitting | C2×Q8×C379 | C2 |
| prime radical | C2×D1516 | C2 |
| hypercenter | C2×Q8 | D379 |
| hypocenter | C379 | #124 |
| LCS | G ▷ C22×C379 ▷ C379 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,379|b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^378,f^b=f^378,f^c=f^3781904 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37565040, #37565417, #37565419, … |
| maximal normal subgroup of | #37565040, #37565417, #37565419, … |
| maximal quotient of | #37565109, #37565134, #37565145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12128, 135);