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C₂×C₄×C₇²×C₂₇ #72189166

order	10584
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 290304
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₇

Aliases

abelian	C₂×C₄×C₇²×C₂₇
multiplicative	(ℤ/10991)ˣ, (ℤ/21982)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉	C₂²×C₃×C₇²
socle, prime radical	C₂²×C₃×C₇²	C₂×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

320 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10584 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇²×C₈×C₂₇, C₄²×C₇²×C₂₇, C₂²×C₄×C₇²×C₂₇, …
maximal normal subgroup of	C₂×C₇²×C₈×C₂₇, C₄²×C₇²×C₂₇, C₂²×C₄×C₇²×C₂₇, …
maximal quotient of	C₂×C₇²×C₈×C₂₇, C₄²×C₇²×C₂₇, C₂²×C₄×C₇²×C₂₇, …
automorphism group of	C₂₉×C₃₇₉
outer automorphism group of	C₂₉×C₃₇₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.