Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C131 ⋊ C2 |
| Sylow | C131 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D131 |
| commutator, socle | C2×C131 | C25 |
| Fitting | H(5,𝔽2)×C131 | C2 |
| hypercenter | H(5,𝔽2) | D131 |
| hypocenter | C131 | #585 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
810 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|e^2=f,b^a=bf,d^a=df,c^b=cf,g^e=g^1301139 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30675306, #30675311, #30675329, … |
| maximal normal subgroup of | #30675306, #30675311, #30675329, … |
| maximal quotient of | #30679159, #30679161, #30679165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 1384);