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C₃×C₄²×C₇×C₂₃ #72186648

order	7728
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 25344
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₃×C₄²×C₇×C₂₃
multiplicative	(ℤ/8033)ˣ, (ℤ/9665)ˣ, (ℤ/16066)ˣ, (ℤ/19330)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₃×C₇×C₂₃
socle, prime radical	C₂²×C₃×C₇×C₂₃	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7728 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₇×C₈×C₂₃, C₂×C₃×C₄²×C₇×C₂₃, C₄²×C₇×C₉×C₂₃, …
maximal normal subgroup of	C₃×C₄×C₇×C₈×C₂₃, C₂×C₃×C₄²×C₇×C₂₃, C₄²×C₇×C₉×C₂₃, …
maximal quotient of	C₃×C₄×C₇×C₈×C₂₃, C₂×C₃×C₄²×C₇×C₂₃, C₄²×C₇×C₉×C₂₃, …
automorphism group of	C₂₉×C₂₇₇, C₅×C₁₉₃₃
outer automorphism group of	C₂₉×C₂₇₇, C₅×C₁₉₃₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.