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#46834248

order	34688
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

C₂₇₁ ⋊ #1296

Subgroups

	subgroup	G/H
center	C₂³	(C₂×D₂₇₁)⋊C₄
commutator	C₂×C₄×C₂₇₁	C₄²
Frattini	C₂×C₄²	C₂×D₂₇₁
Fitting	C₂×C₄⋊C₈×C₂₇₁	C₂
socle, prime radical	C₂³×C₂₇₁	C₂²⋊C₄
cosocle	C₂×C₄²×C₂₇₁	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₇₁
hypocenter	C₂₇₁	#1296
LCS	G ▷ C₂×C₄×C₂₇₁ ▷ C₂²×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 34688

Polycyclic presentation:

2^7,271|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^270,c^b=cg

Conjugacy classes & character table

5438 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34688, 2394);