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#36441343

order	22784
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

C₈₉ ⋊ #7171

Subgroups

	subgroup	G/H
center	C₂²×C₄	D₇₁₂
commutator	C₈×C₈₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₈₉
Fitting	C₂×C₄×C₁₆×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	#102
cosocle	C₂×C₄×C₈×C₈₉	C₂²
hypercenter	C₂×C₄×C₁₆	D₈₉
hypocenter	C₈₉	#7171
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 22784

Polycyclic presentation:

2^8,89|a^2=d,b^2=e,c^2=fh,d^2=g,e^2=fg,f^2=h,b^a=bc,c^a=cf,e^a=efh,f^a=fh,i^a=i^88

Conjugacy classes & character table

5720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 56483);