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C₉×C₁₆×C₁₆₉ #72201633

order	24336
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃²×C₄²×C₁₃ (order 7488) · Inn(G) = C₁ · Out(G) = C₂²×C₃²×C₄²×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₄₃₃₆
abelian	C₉×C₁₆×C₁₆₉
multiplicative	(ℤ/24337)ˣ, (ℤ/48674)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈×C₁₃	C₂×C₃×C₁₃
socle, prime radical	C₂×C₃×C₁₃	C₃×C₈×C₁₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

45 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

24336 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₂₁₆₈, D₂₄₃₃₆
maximal subgroup of	Dic₁₂₁₆₈, D₂₄₃₃₆
maximal normal subgroup of	Dic₁₂₁₆₈, D₂₄₃₃₆
automorphism group of	C₂₄₃₃₇
outer automorphism group of	C₂₄₃₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.