Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C131 ⋊ #346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×D131 |
| commutator | C2×C131 | C4×C8 |
| Fitting | C2×C16×C131 | C2 |
| socle | C22×C131 | C2×C8 |
| hypercenter | C2×C16 | D131 |
| hypocenter | C131 | #346 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C16 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^b=g^1302120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30664096, #346×D131, C2×#22553087, … |
| maximal normal subgroup of | #30664096, #346×D131, C2×#22553087, … |
| maximal quotient of | #30663877, #30663880, #30664038, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 324);