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C₃×C₈×C₉×C₆₄ #72191995

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 884736
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₈

Aliases

abelian	C₃×C₈×C₉×C₆₄
multiplicative	(ℤ/14089)ˣ, (ℤ/28178)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄×C₃₂	C₂²×C₃²
socle, prime radical	C₂²×C₃²	C₃×C₄×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

820 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₈×C₉×C₁₂₈, C₃×C₉×C₁₆×C₆₄, C₂×C₃×C₈×C₉×C₆₄
maximal normal subgroup of	C₃×C₈×C₉×C₁₂₈, C₃×C₉×C₁₆×C₆₄, C₂×C₃×C₈×C₉×C₆₄
maximal quotient of	C₃×C₈×C₉×C₁₂₈, C₃×C₉×C₁₆×C₆₄, C₂×C₃×C₈×C₉×C₆₄
automorphism group of	C₇₃×C₁₉₃
outer automorphism group of	C₇₃×C₁₉₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.