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#360×C₁₃₁ #22552804

order	8384
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃₁ · Schur multiplier (H₂) = C₂

Aliases

#360×C₁₃₁

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃₁	#102
commutator	C₈	C₂×C₄×C₁₃₁
Frattini, cosocle	C₂×C₈	C₂²×C₁₃₁
prime radical	#135×C₁₃₁	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₁ ◁ C₂×C₄×C₁₃₁ ◁ C₂×C₈×C₁₃₁ ◁ G

58 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2096 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#360×D₁₃₁, #30667695, #30667849, …
maximal subgroup of	C₂×#360×C₁₃₁, #2145×C₁₃₁, #2180×C₁₃₁, …
maximal normal subgroup of	C₂×#360×C₁₃₁, #2145×C₁₃₁, #2180×C₁₃₁, …
maximal quotient of	#1333×C₁₃₁, #1334×C₁₃₁, #1347×C₁₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 41);