Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q8×D131 |
| Fitting | C4×Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ C2×C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D131 |
| commutator | C2×C131 | C23×C4 |
| Frattini | C22 | C23×D131 |
| Fitting | C4×Q8×C131 | C2 |
| socle | C22×C131 | C24 |
| hypercenter | C4×Q8 | D131 |
| hypocenter | C131 | C2×C4×Q8 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
298 conjugacy classes of subgroups.
1340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D131, #30664354, #30664388, … |
| maximal normal subgroup of | Q8⋊C8×D131, #30664354, #30664388, … |
| maximal quotient of | C4×C4⋊C4×D131, C4×#16862211, C4×Q8×Dic131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 1012);