Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C131⋊C16) |
| Sylow | C131 ⋊ C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×D131 |
| commutator | C2×C131 | C2×C16 |
| Fitting | C4×C8×C131 | C2 |
| socle | C22×C131 | C2×C8 |
| hypercenter | C4×C8 | D131 |
| hypocenter | C131 | C4⋊C16 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^1302120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊(C131⋊C16), #30663917, #30663919, … |
| maximal normal subgroup of | D4⋊(C131⋊C16), #30663917, #30663919, … |
| maximal quotient of | #30664025, #30664031, #30664039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 368);