Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| isoclinism | isoclinic class of D127 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C42×D127 |
| Fitting | C2×C42×C127 ⋊ C2 |
| derived, Sylow | C127 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D127 |
| commutator, hypocenter | C127 | C22×C42 |
| Frattini | C22 | C23×D127 |
| Fitting | C2×C42×C127 | C2 |
| socle | C23×C127 | C23 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C2×C42 | |
498 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #336×D127, #30638422, #339×D127, … |
| maximal normal subgroup of | #336×D127, #30638422, #339×D127, … |
| maximal quotient of | C43×D127, C2×C42×Dic127, C2×#95×D127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 993);