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C₂³×C₄²×C₄₉ #72185451

order	6272
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2774532096
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

abelian	C₂³×C₄²×C₄₉
multiplicative	(ℤ/23640)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₇	C₂⁵×C₇
socle, prime radical	C₂⁵×C₇	C₂²×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

4500 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6272 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₄×C₈×C₄₉, C₂²×C₄³×C₄₉, C₂⁴×C₄²×C₄₉, …
maximal normal subgroup of	C₂³×C₄×C₈×C₄₉, C₂²×C₄³×C₄₉, C₂⁴×C₄²×C₄₉, …
maximal quotient of	C₂³×C₄×C₈×C₄₉, C₂²×C₄³×C₄₉, C₂⁴×C₄²×C₄₉, …
automorphism group of	C₃×C₅×C₈×C₁₉₇
outer automorphism group of	C₃×C₅×C₈×C₁₉₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.