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C₂²×C₄×C₇×C₈×C₁₇ #72193255

order	15232
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 18874368
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₄×C₇×C₈×C₁₇
multiplicative	(ℤ/31784)ˣ, (ℤ/38120)ˣ, (ℤ/38240)ˣ, (ℤ/45744)ˣ, (ℤ/47676)ˣ, (ℤ/57180)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁴×C₇×C₁₇
socle, prime radical	C₂⁴×C₇×C₁₇	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

1520 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₇×C₁₆×C₁₇, C₂²×C₇×C₈²×C₁₇, C₂×C₄²×C₇×C₈×C₁₇, …
maximal normal subgroup of	C₂²×C₄×C₇×C₁₆×C₁₇, C₂²×C₇×C₈²×C₁₇, C₂×C₄²×C₇×C₈×C₁₇, …
maximal quotient of	C₂²×C₄×C₇×C₁₆×C₁₇, C₂²×C₇×C₈²×C₁₇, C₂×C₄²×C₇×C₈×C₁₇, …
automorphism group of	C₈×C₂₉×C₁₃₇
outer automorphism group of	C₈×C₂₉×C₁₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.