Finite Group Databasebeta

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C₂×C₁₃×C₁₆×C₂₇ #72189709

order	11232
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂×C₁₃×C₁₆×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈×C₉	C₂²×C₃×C₁₃
socle, prime radical	C₂²×C₃×C₁₃	C₈×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

112 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×C₁₃×C₂₇×C₃₂, C₄×C₁₃×C₁₆×C₂₇, C₂²×C₁₃×C₁₆×C₂₇
maximal normal subgroup of	C₂×C₁₃×C₂₇×C₃₂, C₄×C₁₃×C₁₆×C₂₇, C₂²×C₁₃×C₁₆×C₂₇
maximal quotient of	C₂×C₁₃×C₂₇×C₃₂, C₄×C₁₃×C₁₆×C₂₇, C₂²×C₁₃×C₁₆×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.