Finite Group Databasebeta

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C₄₇×#17325 #26057023

order	12032
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₄₇ · Schur multiplier (H₂) = C₂³×C₈

Aliases

C₄₇×#17325

Subgroups

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

772 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 10313);