Finite Group Databasebeta

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C₄×C₄₇×C₈₁ #72193236

order	15228
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₂₃×C₂₇ (order 4968) · Inn(G) = C₁ · Out(G) = C₂³×C₂₃×C₂₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₅₂₂₈
abelian	C₄×C₄₇×C₈₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₂₇	C₂×C₃×C₄₇
socle, prime radical	C₂×C₃×C₄₇	C₂×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15228 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₅₂₂₈, D₃₀₄₅₆
Fitting subgroup of	D₁₅₂₂₈, Dic₇₆₁₄
maximal subgroup of	C₈×C₄₇×C₈₁, C₂×C₄×C₄₇×C₈₁, D₁₅₂₂₈, …
maximal normal subgroup of	C₈×C₄₇×C₈₁, C₂×C₄×C₄₇×C₈₁, D₁₅₂₂₈, …
maximal quotient of	C₈×C₄₇×C₈₁, C₂×C₄×C₄₇×C₈₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.