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C₂×C₈×C₁₆×C₂₉ #20306296

order	7424
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 917504
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₈

Aliases

abelian	C₂×C₈×C₁₆×C₂₉
multiplicative	(ℤ/11883)ˣ, (ℤ/14912)ˣ, (ℤ/15844)ˣ, (ℤ/23766)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₄×C₈	C₂³×C₂₉
socle	C₂³×C₂₉	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

398 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×C₈×C₂₉×C₃₂, C₂×C₁₆²×C₂₉, C₄×C₈×C₁₆×C₂₉, …
maximal normal subgroup of	C₂×C₈×C₂₉×C₃₂, C₂×C₁₆²×C₂₉, C₄×C₈×C₁₆×C₂₉, …
maximal quotient of	C₂×C₈×C₂₉×C₃₂, C₂×C₁₆²×C₂₉, C₄×C₈×C₁₆×C₂₉, …
automorphism group of	C₃×C₁₇×C₂₃₃
outer automorphism group of	C₃×C₁₇×C₂₃₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7424, 4384);