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#26106592

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#1303 ⋊ C₂
Sylow	C₄₇ ⋊ #8098

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1303	C₂
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1303	D₄₇
hypocenter	C₄₇	#8098
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,47|a^2=e,b^2=f,c^2=g,d^2=g,e^2=h,f^2=gh,b^a=bd,d^a=dg,f^a=fgh,c^b=cgh,d^b=dh,i^c=i^46

Conjugacy classes & character table

938 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 59882);