Finite Group Databasebeta

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C₂²×C₃×C₄×C₂₃₃ #72189673

order	11184
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 89088
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₃×C₄×C₂₃₃
multiplicative	(ℤ/16345)ˣ, (ℤ/18213)ˣ, (ℤ/20985)ˣ, (ℤ/21015)ˣ, (ℤ/22376)ˣ, (ℤ/22384)ˣ, (ℤ/24284)ˣ, (ℤ/27980)ˣ, (ℤ/32690)ˣ, (ℤ/33564)ˣ, (ℤ/36426)ˣ, (ℤ/41970)ˣ, (ℤ/42030)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃×C₂₃₃
socle, prime radical	C₂³×C₃×C₂₃₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₈×C₂₃₃, C₂×C₃×C₄²×C₂₃₃, C₂³×C₃×C₄×C₂₃₃
maximal normal subgroup of	C₂²×C₃×C₈×C₂₃₃, C₂×C₃×C₄²×C₂₃₃, C₂³×C₃×C₄×C₂₃₃
maximal quotient of	C₂²×C₃×C₈×C₂₃₃, C₂×C₃×C₄²×C₂₃₃, C₂³×C₃×C₄×C₂₃₃
automorphism group of	C₅×C₇×C₄₆₇
outer automorphism group of	C₅×C₇×C₄₆₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.