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#35212406

order	20864
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

C₁₆₃ ⋊ #1290

Subgroups

	subgroup	G/H
center	C₂²	C₁₆₃⋊#95
commutator	C₂×C₄×C₁₆₃	C₄²
Frattini	C₂×C₄²	C₂×D₁₆₃
Fitting	C₂×C₄⋊C₈×C₁₆₃	C₂
socle	C₂²×C₁₆₃	#95
prime radical	C₂³×C₁₆₃	C₄⋊C₄
cosocle	C₂×C₄²×C₁₆₃	C₂²
hypercenter	C₂×C₄⋊C₈	D₁₆₃
hypocenter	C₁₆₃	#1290
LCS	G ▷ C₂×C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10432

Polycyclic presentation:

2^7,163|a^2=d,b^2=e,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^162,d^b=dg

Conjugacy classes & character table

3272 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 2380);