Finite Group Databasebeta

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C₅×C₈×C₂₃×C₂₇ #72202111

order	24840
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₄×C₉×C₁₁ (order 6336) · Inn(G) = C₁ · Out(G) = C₂⁴×C₄×C₉×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₄₈₄₀
abelian	C₅×C₈×C₂₃×C₂₇
multiplicative	(ℤ/24841)ˣ, (ℤ/49682)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₉	C₂×C₃×C₅×C₂₃
socle, prime radical	C₂×C₃×C₅×C₂₃	C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

24840 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₂₄₂₀, D₂₄₈₄₀
maximal subgroup of	Dic₁₂₄₂₀, D₂₄₈₄₀
maximal normal subgroup of	Dic₁₂₄₂₀, D₂₄₈₄₀
automorphism group of	C₂₄₈₄₁
outer automorphism group of	C₂₄₈₄₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.