Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×C22⋊D127 |
| Fitting | C22×Q8×C127 ⋊ C2 |
| Sylow | C127 ⋊ D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D127 |
| commutator, socle | C22×C127 | C24 |
| Fitting | C22×Q8×C127 | C2 |
| hypercenter | C22×Q8 | D127 |
| hypocenter | C127 | D4×Q8 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1285 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30650233, #30650234, #30650240, … |
| maximal normal subgroup of | #30650233, #30650234, #30650240, … |
| maximal quotient of | Q8×(C2×D127)⋊C4, Q8×C22⋊Dic127, C4⋊C4×C22⋊D127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1213);