Finite Group Databasebeta

← Prev (#44548248) Next (#44548250) →

#44548249

order	32128
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

C₂₅₁ ⋊ #1296

Subgroups

	subgroup	G/H
center	C₂³	(C₂×D₂₅₁)⋊C₄
commutator	C₂×C₄×C₂₅₁	C₄²
Frattini	C₂×C₄²	C₂×D₂₅₁
Fitting	C₂×C₄⋊C₈×C₂₅₁	C₂
socle, prime radical	C₂³×C₂₅₁	C₂²⋊C₄
cosocle	C₂×C₄²×C₂₅₁	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₅₁
hypocenter	C₂₅₁	#1296
LCS	G ▷ C₂×C₄×C₂₅₁ ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 32128

Polycyclic presentation:

2^7,251|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^250,c^b=cg

Conjugacy classes & character table

5038 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 2394);