Finite Group DatabasebetaFinite Group Databasebeta| order | 12128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C379 ⋊ #126 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,379|b^2=de,c^2=d,b^a=bd,c^a=ce,f^c=f^3781904 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D379, C2×#27131324, #37565771, … |
| maximal normal subgroup of | #126×D379, C2×#27131324, #37565771, … |
| maximal quotient of | #37565111, #37565126, #37565129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12128, 139);