Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C131 ⋊ #446 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D131 |
| commutator, socle | C22×C131 | C22×C4 |
| Fitting | #97×C131 | C2 |
| hypercenter | #97 | D131 |
| hypocenter | C131 | #446 |
| LCS | G ▷ C22×C131 ▷ C131 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^b=g^1301328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #446×D131, C2×#22553440, #30674892, … |
| maximal normal subgroup of | #446×D131, C2×#22553440, #30674892, … |
| maximal quotient of | #30665829, #30665833, #30665837, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 677);