Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| isoclinism | isoclinic class of D127 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×Dic127 |
| derived, Sylow | C127 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D127 |
| commutator, hypocenter | C127 | C24×C4 |
| Frattini | C2 | C24×D127 |
| Fitting, socle | C25×C127 | C2 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C25 | |
1362 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30636952, C22×C127⋊#95, C2×C22⋊C4×Dic127, … |
| maximal normal subgroup of | #30636952, C22×C127⋊#95, C2×C22⋊C4×Dic127, … |
| maximal quotient of | C23×C4×Dic127, C23×C22⋊Dic127, C23×C4⋊Dic127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1368);