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C₂²×C₄×C₁₇×C₂₇ #72186366

order	7344
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 55296
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₁₇×C₂₇
multiplicative	(ℤ/13785)ˣ, (ℤ/14704)ˣ, (ℤ/18380)ˣ, (ℤ/27570)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉	C₂³×C₃×C₁₇
socle, prime radical	C₂³×C₃×C₁₇	C₂×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7344 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₈×C₁₇×C₂₇, C₂×C₄²×C₁₇×C₂₇, C₂³×C₄×C₁₇×C₂₇, …
maximal normal subgroup of	C₂²×C₈×C₁₇×C₂₇, C₂×C₄²×C₁₇×C₂₇, C₂³×C₄×C₁₇×C₂₇, …
maximal quotient of	C₂²×C₈×C₁₇×C₂₇, C₂×C₄²×C₁₇×C₂₇, C₂³×C₄×C₁₇×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.