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#350×C₁₄₉ #23749107

order	9536
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₄₉ · Schur multiplier (H₂) = C₂

Aliases

#350×C₁₄₉

Subgroups

	subgroup	G/H
center	C₈×C₁₄₉	D₄
commutator	C₄	C₂×C₈×C₁₄₉
Frattini, cosocle	C₂×C₈	C₂²×C₁₄₉
socle	C₂×C₁₄₉	C₂²⋊C₈
prime radical	#41×C₁₄₉	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₄₉ ◁ C₂×C₈×C₁₄₉ ◁ G

56 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	#350×D₁₄₉, #34046317, #34046525, …
maximal subgroup of	C₂×#350×C₁₄₉, #2117×C₁₄₉, #2170×C₁₄₉, …
maximal normal subgroup of	C₂×#350×C₁₄₉, #2117×C₁₄₉, #2170×C₁₄₉, …
maximal quotient of	#1315×C₁₄₉, #1323×C₁₄₉, D₄⋊C₁₆×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 31);