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#44548235

order	32128
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

C₂₅₁ ⋊ #1290

Subgroups

	subgroup	G/H
center	C₂²	C₂₅₁⋊#95
commutator	C₂×C₄×C₂₅₁	C₄²
Frattini	C₂×C₄²	C₂×D₂₅₁
Fitting	C₂×C₄⋊C₈×C₂₅₁	C₂
socle	C₂²×C₂₅₁	#95
prime radical	C₂³×C₂₅₁	C₄⋊C₄
cosocle	C₂×C₄²×C₂₅₁	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₅₁
hypocenter	C₂₅₁	#1290
LCS	G ▷ C₂×C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16064

Polycyclic presentation:

2^7,251|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^250,d^b=dg

Conjugacy classes & character table

5032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 2380);