Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C131⋊#338 |
| Sylow | C131 ⋊ #338 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×Dic131 |
| commutator | C4×C131 | C42 |
| Frattini | C22×C4 | C2×D131 |
| Fitting | C2×M16×C131 | C2 |
| socle | C2×C131 | #95 |
| hypercenter | C2×M16 | D131 |
| hypocenter | C131 | #338 |
| LCS | G ▷ C4×C131 ▷ C131 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,e^a=ef,d^b=df,g^b=g^1301322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30663952, #30663953, #30663955, … |
| maximal normal subgroup of | #30663952, #30663953, #30663955, … |
| maximal quotient of | #30663791, #30663792, #30663832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 307);