Finite Group Databasebeta

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C₂²×C₃×C₄×C₂₈₉ #72192089

order	13872
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 104448
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₃×C₄×C₂₈₉
multiplicative	(ℤ/27752)ˣ, (ℤ/41628)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₇	C₂³×C₃×C₁₇
socle, prime radical	C₂³×C₃×C₁₇	C₂×C₁₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13872 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₈×C₂₈₉, C₂×C₃×C₄²×C₂₈₉, C₂³×C₃×C₄×C₂₈₉
maximal normal subgroup of	C₂²×C₃×C₈×C₂₈₉, C₂×C₃×C₄²×C₂₈₉, C₂³×C₃×C₄×C₂₈₉
maximal quotient of	C₂²×C₃×C₈×C₂₈₉, C₂×C₃×C₄²×C₂₈₉, C₂³×C₃×C₄×C₂₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.