Finite Group Databasebeta

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C₂×C₅×C₇×C₁₃×C₂₇ #72201809

order	24570
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃²×C₄²×C₉ (order 5184) · Inn(G) = C₁ · Out(G) = C₂²×C₃²×C₄²×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₄₅₇₀
abelian	C₂×C₅×C₇×C₁₃×C₂₇
multiplicative	(ℤ/24571)ˣ, (ℤ/49142)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃×C₅×C₇×C₁₃
socle, prime radical	C₂×C₃×C₅×C₇×C₁₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

24570 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₂₂₈₅, C₂×D₁₂₂₈₅
maximal subgroup of	Dic₁₂₂₈₅, C₂×D₁₂₂₈₅
maximal normal subgroup of	Dic₁₂₂₈₅, C₂×D₁₂₂₈₅
automorphism group of	C₂₄₅₇₁
outer automorphism group of	C₂₄₅₇₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.