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C₂×C₄²×C₈×C₂₉ #20315225

order	7424
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 176160768
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄³

Aliases

abelian	C₂×C₄²×C₈×C₂₉
multiplicative	(ℤ/18640)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂²×C₄	C₂⁴×C₂₉
socle	C₂⁴×C₂₉	C₂²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

2046 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	C₂×C₄²×C₁₆×C₂₉, C₂×C₄×C₈²×C₂₉, C₄³×C₈×C₂₉, …
maximal normal subgroup of	C₂×C₄²×C₁₆×C₂₉, C₂×C₄×C₈²×C₂₉, C₄³×C₈×C₂₉, …
maximal quotient of	C₂×C₄²×C₁₆×C₂₉, C₂×C₄×C₈²×C₂₉, C₄³×C₈×C₂₉, …
automorphism group of	C₅×C₁₆×C₂₃₃
outer automorphism group of	C₅×C₁₆×C₂₃₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7424, 13313);