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C₂×C₃×C₄²×C₄₇ #72183997

order	4512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 141312
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₃×C₄²×C₄₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂³×C₃×C₄₇
socle, prime radical	C₂³×C₃×C₄₇	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₈×C₄₇, C₃×C₄³×C₄₇, C₂²×C₃×C₄²×C₄₇, …
maximal normal subgroup of	C₂×C₃×C₄×C₈×C₄₇, C₃×C₄³×C₄₇, C₂²×C₃×C₄²×C₄₇, …
maximal quotient of	C₂×C₃×C₄×C₈×C₄₇, C₃×C₄³×C₄₇, C₂²×C₃×C₄²×C₄₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.