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C₂²×C₁₃×C₁₆×C₁₇ #72192303

order	14144
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 147456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₁₃×C₁₆×C₁₇
multiplicative	(ℤ/22593)ˣ, (ℤ/28352)ˣ, (ℤ/30124)ˣ, (ℤ/45186)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂³×C₁₃×C₁₇
socle, prime radical	C₂³×C₁₃×C₁₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14144 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₁₃×C₁₇×C₃₂, C₂×C₄×C₁₃×C₁₆×C₁₇, C₂³×C₁₃×C₁₆×C₁₇
maximal normal subgroup of	C₂²×C₁₃×C₁₇×C₃₂, C₂×C₄×C₁₃×C₁₆×C₁₇, C₂³×C₁₃×C₁₆×C₁₇
maximal quotient of	C₂²×C₁₃×C₁₇×C₃₂, C₂×C₄×C₁₃×C₁₆×C₁₇, C₂³×C₁₃×C₁₆×C₁₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.