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C₂×C₃×C₄×C₂₂₃ #72184666

order	5352
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3552
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₂₂₃
multiplicative	(ℤ/8031)ˣ, (ℤ/10708)ˣ, (ℤ/16062)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₂₂₃
socle, prime radical	C₂²×C₃×C₂₂₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₂₂₃, C₃×C₄²×C₂₂₃, C₂²×C₃×C₄×C₂₂₃, …
maximal normal subgroup of	C₂×C₃×C₈×C₂₂₃, C₃×C₄²×C₂₂₃, C₂²×C₃×C₄×C₂₂₃, …
maximal quotient of	C₂×C₃×C₈×C₂₂₃, C₃×C₄²×C₂₂₃, C₂²×C₃×C₄×C₂₂₃, …
automorphism group of	C₃×C₂₆₇₇, C₄×C₂₆₇₇
outer automorphism group of	C₃×C₂₆₇₇, C₄×C₂₆₇₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.