Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×C131⋊C16 |
| derived, Sylow | C131 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D131 |
| commutator, hypocenter | C131 | C4×C16 |
| Frattini | C2×C8 | C2×D131 |
| Fitting | C4×C8×C131 | C2 |
| socle | C22×C131 | C2×C8 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C4×C8 | |
58 conjugacy classes of subgroups.
2144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×C131⋊C8, C8×C131⋊C16, #30663877, … |
| maximal normal subgroup of | C16×C131⋊C8, C8×C131⋊C16, #30663877, … |
| maximal quotient of | C8×C131⋊C16, #30663879, #30664039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 323);