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C₃×C₄²×C₂₈₉ #72192087

order	13872
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 52224
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₃×C₄²×C₂₈₉
multiplicative	(ℤ/17345)ˣ, (ℤ/34690)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₁₇	C₂²×C₃×C₁₇
socle, prime radical	C₂²×C₃×C₁₇	C₂²×C₁₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13872 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₈×C₂₈₉, C₂×C₃×C₄²×C₂₈₉
maximal normal subgroup of	C₃×C₄×C₈×C₂₈₉, C₂×C₃×C₄²×C₂₈₉
maximal quotient of	C₃×C₄×C₈×C₂₈₉, C₂×C₃×C₄²×C₂₈₉
automorphism group of	C₅×C₃₄₆₉
outer automorphism group of	C₅×C₃₄₆₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.