Finite Group Databasebeta

← Prev (#72186876) Next (#72186878) →

C₂³×C₃×C₉×C₃₇ #72186877

order	7992
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 653184
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃

Aliases

abelian	C₂³×C₃×C₉×C₃₇
multiplicative	(ℤ/12711)ˣ, (ℤ/16948)ˣ, (ℤ/24084)ˣ, (ℤ/25422)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂³×C₃²×C₃₇
socle, prime radical	C₂³×C₃²×C₃₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

320 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7992 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₄×C₉×C₃₇, C₂⁴×C₃×C₉×C₃₇, C₂³×C₃×C₂₇×C₃₇, …
maximal normal subgroup of	C₂²×C₃×C₄×C₉×C₃₇, C₂⁴×C₃×C₉×C₃₇, C₂³×C₃×C₂₇×C₃₇, …
maximal quotient of	C₂²×C₃×C₄×C₉×C₃₇, C₂⁴×C₃×C₉×C₃₇, C₂³×C₃×C₂₇×C₃₇, …
automorphism group of	C₄×C₂₇×C₂₂₃
outer automorphism group of	C₄×C₂₇×C₂₂₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.