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C₄×C₉×C₁₇₃ #20261986

order	6228
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄×C₄₃ (order 2064) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄×C₄₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₆₂₂₈
abelian	C₄×C₉×C₁₇₃
multiplicative	(ℤ/6229)ˣ, (ℤ/12458)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂×C₃	C₂×C₃×C₁₇₃
socle	C₂×C₃×C₁₇₃	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6228 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₅×C₉×C₁₇₃, C₉×Dic₅×C₁₇₃, C₉×AGL(1,𝔽₅)×C₁₇₃, …
maximal normal subgroup of	C₄×C₅×C₉×C₁₇₃, C₈×C₉×C₁₇₃, C₂×C₄×C₉×C₁₇₃, …
maximal quotient of	C₄×C₅×C₉×C₁₇₃, C₉×Dic₅×C₁₇₃, C₉×AGL(1,𝔽₅)×C₁₇₃, …
automorphism group of	C₆₂₂₉, C₂×C₆₂₂₉
outer automorphism group of	C₆₂₂₉, C₂×C₆₂₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6228, 1);