#36474031

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

Fitting	C₈₉×#1380 ⋊ C₂
Sylow	C₈₉ ⋊ #13449

Subgroups

	subgroup	G/H
center	C₂³	D₈×D₈₉
commutator, cosocle	C₂²×C₈×C₈₉	C₂³
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₈₉×#1380	C₂
socle	C₂³×C₈₉	C₂×D₈
prime radical	C₂²×D₇₁₂	C₂²
hypercenter	#1380	D₈₉
hypocenter	C₈₉	#13449
LCS	G ▷ C₂²×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1380

446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11392

Polycyclic presentation:

2^8,89|a^2=h,c^2=d,d^2=gh,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fgh,g^a=gh,i^a=i^88,c^b=cf,d^b=dg,e^b=egh,f^b=fgh,g^b=gh,i^b=i^88,i^c=i^88

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 89171);