Finite Group Databasebeta

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C₂²×C₃²×C₄×C₈×C₉ #72189018

order	10368
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4586471424
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₃³×C₄

Aliases

abelian	C₂²×C₃²×C₄×C₈×C₉
multiplicative	(ℤ/19929)ˣ, (ℤ/22995)ˣ, (ℤ/26572)ˣ, (ℤ/34164)ˣ, (ℤ/39858)ˣ, (ℤ/45990)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃³
socle, prime radical	C₂⁴×C₃³	C₂×C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

19000 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃²×C₄×C₉×C₁₆, C₂²×C₃²×C₈²×C₉, C₂×C₃²×C₄²×C₈×C₉, …
maximal normal subgroup of	C₂²×C₃²×C₄×C₉×C₁₆, C₂²×C₃²×C₈²×C₉, C₂×C₃²×C₄²×C₈×C₉, …
maximal quotient of	C₂²×C₃²×C₄×C₉×C₁₆, C₂²×C₃²×C₈²×C₉, C₂×C₃²×C₄²×C₈×C₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.