Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×C131⋊C8 |
| derived, Sylow | C131 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D131 |
| commutator, hypocenter | C131 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D131 |
| Fitting | C2×C42×C131 | C2 |
| socle | C23×C131 | C2×C4 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C2×C42 | |
162 conjugacy classes of subgroups.
2144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131⋊#1273, #30663795, #30663797, … |
| maximal normal subgroup of | C131⋊#1273, #30663795, #30663797, … |
| maximal quotient of | C2×C8×C131⋊C8, C2×#22553033, M16×C131⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 495);