Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C137 ⋊ C2 |
| Sylow | C137 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D137 |
| commutator, socle | C2×C137 | C25 |
| Fitting | H(5,𝔽2)×C137 | C2 |
| hypercenter | H(5,𝔽2) | D137 |
| hypocenter | C137 | #585 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
810 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|e^2=f,b^a=bf,d^a=df,c^b=cf,g^e=g^1361190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31790134, #31790139, #31790157, … |
| maximal normal subgroup of | #31790134, #31790139, #31790157, … |
| maximal quotient of | #31793987, #31793989, #31793993, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1384);