Finite Group Databasebeta

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C₂×C₈×C₂₇×C₃₂ #72192006

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1179648
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₈

Aliases

C₂×C₈×C₂₇×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₉×C₁₆	C₂³×C₃
socle, prime radical	C₂³×C₃	C₄×C₉×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

1032 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×C₈×C₂₇×C₆₄, C₂×C₁₆×C₂₇×C₃₂, C₄×C₈×C₂₇×C₃₂, …
maximal normal subgroup of	C₂×C₈×C₂₇×C₆₄, C₂×C₁₆×C₂₇×C₃₂, C₄×C₈×C₂₇×C₃₂, …
maximal quotient of	C₂×C₈×C₂₇×C₆₄, C₂×C₁₆×C₂₇×C₃₂, C₄×C₈×C₂₇×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.