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C₂×C₁₆²×C₂₇ #72192018

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7077888
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₁₆

Aliases

abelian	C₂×C₁₆²×C₂₇
multiplicative	(ℤ/22083)ˣ, (ℤ/27712)ˣ, (ℤ/29444)ˣ, (ℤ/44166)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈²×C₉	C₂³×C₃
socle, prime radical	C₂³×C₃	C₈²×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

1288 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₆×C₂₇×C₃₂, C₄×C₁₆²×C₂₇, C₂²×C₁₆²×C₂₇
maximal normal subgroup of	C₂×C₁₆×C₂₇×C₃₂, C₄×C₁₆²×C₂₇, C₂²×C₁₆²×C₂₇
maximal quotient of	C₂×C₁₆×C₂₇×C₃₂, C₄×C₁₆²×C₂₇, C₂²×C₁₆²×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.