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C₂³×C₄×C₈×C₂₇ #72186013

order	6912
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1585446912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

C₂³×C₄×C₈×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄×C₉	C₂⁵×C₃
socle, prime radical	C₂⁵×C₃	C₂×C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

9276 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6912 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₄×C₁₆×C₂₇, C₂³×C₈²×C₂₇, C₂²×C₄²×C₈×C₂₇, …
maximal normal subgroup of	C₂³×C₄×C₁₆×C₂₇, C₂³×C₈²×C₂₇, C₂²×C₄²×C₈×C₂₇, …
maximal quotient of	C₂³×C₄×C₁₆×C₂₇, C₂³×C₈²×C₂₇, C₂²×C₄²×C₈×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.