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C₃²×C₄²×C₇² #72186131

order	7056
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 9289728
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄×C₇

Aliases

C₃²×C₄²×C₇²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₃²×C₇²
socle, prime radical	C₂²×C₃²×C₇²	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

900 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7056 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄×C₇²×C₈, C₂×C₃²×C₄²×C₇², C₃×C₄²×C₇²×C₉, …
maximal normal subgroup of	C₃²×C₄×C₇²×C₈, C₂×C₃²×C₄²×C₇², C₃×C₄²×C₇²×C₉, …
maximal quotient of	C₃²×C₄×C₇²×C₈, C₂×C₃²×C₄²×C₇², C₃×C₄²×C₇²×C₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.