Finite Group Databasebeta

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C₂×C₄×C₁₆×C₁₂₁ #72193479

order	15488
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 450560
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₄×C₁₆×C₁₂₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈×C₁₁	C₂³×C₁₁
socle, prime radical	C₂³×C₁₁	C₂×C₈×C₁₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15488 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₃₂×C₁₂₁, C₂×C₈×C₁₆×C₁₂₁, C₄²×C₁₆×C₁₂₁, …
maximal normal subgroup of	C₂×C₄×C₃₂×C₁₂₁, C₂×C₈×C₁₆×C₁₂₁, C₄²×C₁₆×C₁₂₁, …
maximal quotient of	C₂×C₄×C₃₂×C₁₂₁, C₂×C₈×C₁₆×C₁₂₁, C₄²×C₁₆×C₁₂₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.