#30603103

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

No aliases for this group.

Splittings

Fitting	C₂×C₂²⋊C₈×C₆₁ ⋊ C₄
Sylow	C₆₁ ⋊ #10961

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊#6923
commutator	C₂³×C₆₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#6923
Fitting	C₂×C₂²⋊C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₄×C₂²⋊C₄
prime radical	C₂²×#11758222	C₂²
cosocle	C₂²×C₄×D₆₁	C₂³
hypercenter	C₂×C₂²⋊C₈	#6923
hypocenter	C₆₁	#10961
LCS	G ▷ C₂³×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₂²⋊C₈

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3904

Polycyclic presentation:

2^8,61|a^2=f,b^2=g,c^2=ef,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,i^a=i^50,d^b=dh,e^b=eh,f^b=fh,i^b=i^50,d^c=dh,e^c=eh,f^c=fh,i^c=i^11,i^f=i^60,i^g=i^60

Conjugacy classes & character table

664 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1092658);