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C₂×C₅²×C₈×C₂₇ #72189339

order	10800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 138240
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

abelian	C₂×C₅²×C₈×C₂₇
multiplicative	(ℤ/11111)ˣ, (ℤ/22222)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₉	C₂²×C₃×C₅²
socle, prime radical	C₂²×C₃×C₅²	C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

352 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅²×C₁₆×C₂₇, C₄×C₅²×C₈×C₂₇, C₂²×C₅²×C₈×C₂₇, …
maximal normal subgroup of	C₂×C₅²×C₁₆×C₂₇, C₄×C₅²×C₈×C₂₇, C₂²×C₅²×C₈×C₂₇, …
maximal quotient of	C₂×C₅²×C₁₆×C₂₇, C₄×C₅²×C₈×C₂₇, C₂²×C₅²×C₈×C₂₇, …
automorphism group of	C₄₁×C₂₇₁
outer automorphism group of	C₄₁×C₂₇₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.