Finite Group Databasebeta

← Prev (#20328219) Next (#20328221) →

C₂²×C₄×C₁₆×C₂₉ #20328220

order	7424
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 11010048
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₄×C₁₆×C₂₉
multiplicative	(ℤ/15045)ˣ, (ℤ/16048)ˣ, (ℤ/18880)ˣ, (ℤ/20060)ˣ, (ℤ/30090)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂×C₈	C₂⁴×C₂₉
socle	C₂⁴×C₂₉	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

1022 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7424 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₂₉×C₃₂, C₂²×C₈×C₁₆×C₂₉, C₂×C₄²×C₁₆×C₂₉, …
maximal normal subgroup of	C₂²×C₄×C₂₉×C₃₂, C₂²×C₈×C₁₆×C₂₉, C₂×C₄²×C₁₆×C₂₉, …
maximal quotient of	C₂²×C₄×C₂₉×C₃₂, C₂²×C₈×C₁₆×C₂₉, C₂×C₄²×C₁₆×C₂₉, …
automorphism group of	C₁₆×C₁₇×C₅₉, C₅×C₅₉×C₆₄
outer automorphism group of	C₁₆×C₁₇×C₅₉, C₅×C₅₉×C₆₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7424, 26308);