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#36459997

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

Splittings

C₈₉ ⋊ #10789

Subgroups

	subgroup	G/H
center	C₂⁴	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₂²×#103×C₈₉	C₂
socle, prime radical	C₂⁴×C₈₉	C₂×D₄
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂²×#103	D₈₉
hypocenter	C₈₉	#10789
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×#103

1370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 22784

Polycyclic presentation:

2^8,89|a^2=f,b^2=g,c^2=h,d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,d^b=dh,e^b=eh,i^b=i^88,d^c=dh,e^c=eh

Conjugacy classes & character table

2540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 75137);