Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C131 ⋊ #322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C2×D131 |
| commutator | C2×C131 | C4×C8 |
| Fitting | C4×C8×C131 | C2 |
| socle | C22×C131 | C42 |
| hypercenter | C4×C8 | D131 |
| hypocenter | C131 | #322 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^a=g^1302120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #322×D131, C2×#22553034, C8×#14523496, … |
| maximal normal subgroup of | #322×D131, C2×#22553034, C8×#14523496, … |
| maximal quotient of | C131⋊#1273, #30663880, #30663882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 271);