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C₂×C₃×C₄×C₁₃×C₄₉ #72193297

order	15288
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8064
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₁₃×C₄₉
multiplicative	(ℤ/15563)ˣ, (ℤ/17843)ˣ, (ℤ/18179)ˣ, (ℤ/19115)ˣ, (ℤ/22941)ˣ, (ℤ/31126)ˣ, (ℤ/35686)ˣ, (ℤ/36358)ˣ, (ℤ/38230)ˣ, (ℤ/45882)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₇	C₂²×C₃×C₇×C₁₃
socle, prime radical	C₂²×C₃×C₇×C₁₃	C₂×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₁₃×C₄₉, C₃×C₄²×C₁₃×C₄₉, C₂²×C₃×C₄×C₁₃×C₄₉
maximal normal subgroup of	C₂×C₃×C₈×C₁₃×C₄₉, C₃×C₄²×C₁₃×C₄₉, C₂²×C₃×C₄×C₁₃×C₄₉
maximal quotient of	C₂×C₃×C₈×C₁₃×C₄₉, C₃×C₄²×C₁₃×C₄₉, C₂²×C₃×C₄×C₁₃×C₄₉
automorphism group of	C₇₉×C₁₉₇, C₇×C₂₅₄₉
outer automorphism group of	C₇₉×C₁₉₇, C₇×C₂₅₄₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.