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C₂×C₄²×C₁₃×C₂₇ #72189717

order	11232
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 331776
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

abelian	C₂×C₄²×C₁₃×C₂₇
multiplicative	(ℤ/17331)ˣ, (ℤ/21465)ˣ, (ℤ/23108)ˣ, (ℤ/34662)ˣ, (ℤ/42930)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₉	C₂³×C₃×C₁₃
socle, prime radical	C₂³×C₃×C₁₃	C₂²×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₈×C₁₃×C₂₇, C₄³×C₁₃×C₂₇, C₂²×C₄²×C₁₃×C₂₇
maximal normal subgroup of	C₂×C₄×C₈×C₁₃×C₂₇, C₄³×C₁₃×C₂₇, C₂²×C₄²×C₁₃×C₂₇
maximal quotient of	C₂×C₄×C₈×C₁₃×C₂₇, C₄³×C₁₃×C₂₇, C₂²×C₄²×C₁₃×C₂₇
automorphism group of	C₅×C₅₃×C₈₁
outer automorphism group of	C₅×C₅₃×C₈₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.