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#34066985

order	19328
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

C₁₅₁ ⋊ #1292

Subgroups

	subgroup	G/H
center	C₂²	C₁₅₁⋊#95
commutator	C₂×C₄×C₁₅₁	C₄²
Frattini	C₂×C₄²	C₂×D₁₅₁
Fitting	C₂×C₄⋊C₈×C₁₅₁	C₂
socle	C₂²×C₁₅₁	#95
prime radical	C₂³×C₁₅₁	C₄⋊C₄
cosocle	C₂×C₄²×C₁₅₁	C₂²
hypercenter	C₂×C₄⋊C₈	D₁₅₁
hypocenter	C₁₅₁	#1292
LCS	G ▷ C₂×C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9664

Polycyclic presentation:

2^7,151|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^150,d^b=dg

Conjugacy classes & character table

3032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 2385);