Finite Group Databasebeta

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C₄×C₁₃×C₁₇×C₂₇ #72201160

order	23868
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄×C₉×C₁₆ (order 6912) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄×C₉×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₃₈₆₈
abelian	C₄×C₁₃×C₁₇×C₂₇
multiplicative	(ℤ/23869)ˣ, (ℤ/47738)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉	C₂×C₃×C₁₃×C₁₇
socle, prime radical	C₂×C₃×C₁₃×C₁₇	C₂×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

23868 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₁₉₃₄, D₂₃₈₆₈
maximal subgroup of	Dic₁₁₉₃₄, D₂₃₈₆₈
maximal normal subgroup of	Dic₁₁₉₃₄, D₂₃₈₆₈
automorphism group of	C₂₃₈₆₉
outer automorphism group of	C₂₃₈₆₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.