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#433×C₁₄₉ #23749190

order	9536
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₄₉ · Schur multiplier (H₂) = C₄

Aliases

#433×C₁₄₉

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₄₉	C₂³
commutator	C₂²	C₂²×C₄×C₁₄₉
Frattini, cosocle	C₂×C₄	C₂³×C₁₄₉
socle	C₂²×C₁₄₉	C₂²×C₄
prime radical	C₂³×C₁₄₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4172 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#433×D₁₄₉, #34053325, #34053332, …
maximal subgroup of	C₂×#433×C₁₄₉, #2921×C₁₄₉, #2922×C₁₄₉, …
maximal normal subgroup of	C₂×#433×C₁₄₉, #2921×C₁₄₉, #2922×C₁₄₉, …
maximal quotient of	#1746×C₁₄₉, #1750×C₁₄₉, #1768×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 114);