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C₃×C₄³×C₇×C₉ #72190487

order	12096
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 55738368
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄³

Aliases

abelian	C₃×C₄³×C₇×C₉
multiplicative	(ℤ/13949)ˣ, (ℤ/27898)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³×C₃	C₂³×C₃²×C₇
socle, prime radical	C₂³×C₃²×C₇	C₂³×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

2580 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₇×C₈×C₉, C₂×C₃×C₄³×C₇×C₉
maximal normal subgroup of	C₃×C₄²×C₇×C₈×C₉, C₂×C₃×C₄³×C₇×C₉
maximal quotient of	C₃×C₄²×C₇×C₈×C₉, C₂×C₃×C₄³×C₇×C₉
automorphism group of	C₁₃×C₂₉×C₃₇
outer automorphism group of	C₁₃×C₂₉×C₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.