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C₂×C₄×C₈×C₉×C₁₃ #72186459

order	7488
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 147456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

abelian	C₂×C₄×C₈×C₉×C₁₃
multiplicative	(ℤ/11607)ˣ, (ℤ/14055)ˣ, (ℤ/14992)ˣ, (ℤ/15476)ˣ, (ℤ/18740)ˣ, (ℤ/23214)ˣ, (ℤ/28110)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₄	C₂³×C₃×C₁₃
socle, prime radical	C₂³×C₃×C₁₃	C₂×C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

486 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7488 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₉×C₁₃×C₁₆, C₂×C₈²×C₉×C₁₃, C₄²×C₈×C₉×C₁₃, …
maximal normal subgroup of	C₂×C₄×C₉×C₁₃×C₁₆, C₂×C₈²×C₉×C₁₃, C₄²×C₈×C₉×C₁₃, …
maximal quotient of	C₂×C₄×C₉×C₁₃×C₁₆, C₂×C₈²×C₉×C₁₃, C₄²×C₈×C₉×C₁₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.