Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C131 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×D131 |
| commutator, socle | C2×C131 | C2×C16 |
| Fitting | C2×C16×C131 | C2 |
| hypercenter | C2×C16 | D131 |
| hypocenter | C131 | M64 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C16 ◁ C2×C16 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^1302120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30664096, #30664097, #30664100, … |
| maximal normal subgroup of | #30664096, #30664097, #30664100, … |
| maximal quotient of | #30664095, C22⋊(C131⋊C32), C4⋊(C131⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 383);