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#361×C₁₄₉ #23749118

order	9536
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₄₉ · Schur multiplier (H₂) = C₂

Aliases

#361×C₁₄₉

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₄₉	#102
commutator	C₈	C₂×C₄×C₁₄₉
Frattini, cosocle	C₂×C₈	C₂²×C₁₄₉
prime radical	C₂×D₈×C₁₄₉	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₄₉ ◁ C₂×C₄×C₁₄₉ ◁ C₂×C₈×C₁₄₉ ◁ G

62 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#361×D₁₄₉, #34046437, #34046592, …
maximal subgroup of	C₂×#361×C₁₄₉, #2148×C₁₄₉, AGL(1,ℤ/16)×C₁₄₉, …
maximal normal subgroup of	C₂×#361×C₁₄₉, #2148×C₁₄₉, AGL(1,ℤ/16)×C₁₄₉, …
maximal quotient of	#1333×C₁₄₉, #1349×C₁₄₉, #1361×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 42);