Finite Group Databasebeta

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C₄₇×#20364 #26060062

order	12032
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₄₇ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

C₄₇×#20364

Subgroups

	subgroup	G/H
center	C₂×C₄²×C₄₇	C₂³
commutator	C₂²	C₂²×C₄²×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₄₇ ◁ G

1286 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 13352);