Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C131 ⋊ H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×Dic131 |
| commutator | C4×C131 | C42 |
| Frattini | C22×C4 | C2×D131 |
| Fitting | #117×C131 | C2 |
| socle | C2×C131 | #95 |
| hypercenter | #117 | D131 |
| hypocenter | C131 | H(3,ℤ/4) |
| LCS | G ▷ C4×C131 ▷ C131 | |
| UCS | C1 ◁ C4 ◁ #117 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,b^2=e,c^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 | H(3,ℤ/4)×D131, C2×#22553068, #30665715, … |
| maximal normal subgroup of | H(3,ℤ/4)×D131, C2×#22553068, #30665715, … |
| maximal quotient of | #30663789, #30663790, #30663791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 305);