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C₂×C₃×C₄×C₅×C₇×C₂₃ #72197007

order	19320
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8448
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₅×C₇×C₂₃
multiplicative	(ℤ/19667)ˣ, (ℤ/19787)ˣ, (ℤ/19823)ˣ, (ℤ/20039)ˣ, (ℤ/21263)ˣ, (ℤ/22547)ˣ, (ℤ/22589)ˣ, (ℤ/24155)ˣ, (ℤ/24175)ˣ, (ℤ/28983)ˣ, (ℤ/28989)ˣ, (ℤ/38644)ˣ, (ℤ/39334)ˣ, (ℤ/39574)ˣ, (ℤ/39646)ˣ, (ℤ/40078)ˣ, (ℤ/42526)ˣ, (ℤ/45094)ˣ, (ℤ/45178)ˣ, (ℤ/48310)ˣ, (ℤ/48350)ˣ, (ℤ/57966)ˣ, (ℤ/57978)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₅×C₇×C₂₃
socle, prime radical	C₂²×C₃×C₅×C₇×C₂₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

19320 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₇₁×C₂₇₇, C₄₇×C₄₂₁, C₄₃×C₄₆₁, …
outer automorphism group of	C₇₁×C₂₇₇, C₄₇×C₄₂₁, C₄₃×C₄₆₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.