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#332×C₁₄₉ #23749089

order	9536
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₄₉ · Schur multiplier (H₂) = C₂

Aliases

#332×C₁₄₉

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₄₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄×C₁₄₉
Frattini, cosocle	C₄²	C₂²×C₁₄₉
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₄²×C₁₄₉ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2831 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#332×D₁₄₉, #34043339, #34043347, …
maximal subgroup of	C₂×#332×C₁₄₉, #1540×C₁₄₉, #1542×C₁₄₉, …
maximal normal subgroup of	C₂×#332×C₁₄₉, #1540×C₁₄₉, #1542×C₁₄₉, …
maximal quotient of	#1271×C₁₄₉, #1296×C₁₄₉, #1363×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 13);