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#360×C₁₄₉ #23749117

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

Aliases

#360×C₁₄₉

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₄₉	#102
commutator	C₈	C₂×C₄×C₁₄₉
Frattini, cosocle	C₂×C₈	C₂²×C₁₄₉
prime radical	#135×C₁₄₉	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₄₉ ◁ C₂×C₄×C₁₄₉ ◁ C₂×C₈×C₁₄₉ ◁ G

58 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	#360×D₁₄₉, #34046425, #34046579, …
maximal subgroup of	C₂×#360×C₁₄₉, #2145×C₁₄₉, #2180×C₁₄₉, …
maximal normal subgroup of	C₂×#360×C₁₄₉, #2145×C₁₄₉, #2180×C₁₄₉, …
maximal quotient of	#1333×C₁₄₉, #1334×C₁₄₉, #1347×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 41);