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C₂⁴×C₄²×C₇×C₉ #72194115

order	16128
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4566087106560
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

abelian	C₂⁴×C₄²×C₇×C₉
multiplicative	(ℤ/66120)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂⁶×C₃×C₇
socle, prime radical	C₂⁶×C₃×C₇	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

72090 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16128 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₄×C₇×C₈×C₉, C₂³×C₄³×C₇×C₉, C₂⁵×C₄²×C₇×C₉
maximal normal subgroup of	C₂⁴×C₄×C₇×C₈×C₉, C₂³×C₄³×C₇×C₉, C₂⁵×C₄²×C₇×C₉
maximal quotient of	C₂⁴×C₄×C₇×C₈×C₉, C₂³×C₄³×C₇×C₉, C₂⁵×C₄²×C₇×C₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.