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C₂×C₂₃×#1400 #19161181

order	5888
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₂₃×#1400

Subgroups

	subgroup	G/H
center	C₂×C₈×C₂₃	C₂²⋊C₄
commutator	C₂²	C₂²×C₁₆×C₂₃
Frattini, cosocle	C₂×C₁₆	C₂³×C₂₃
socle	C₂²×C₂₃	C₂²⋊C₁₆
prime radical	C₂⁴×C₂₃	C₁₆
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₃ ◁ C₂²×C₁₆×C₂₃ ◁ G

306 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5888, 6543);