Finite Group Databasebeta

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#104×C₃₅₉ #26039880

order	11488
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₃₅₉ · Schur multiplier (H₂) = C₂

Aliases

#104×C₃₅₉

Subgroups

	subgroup	G/H
center	C₄×C₃₅₉	D₄
commutator	C₄	C₂×C₄×C₃₅₉
Frattini, cosocle	C₂×C₄	C₂²×C₃₅₉
socle	C₂×C₃₅₉	C₂²⋊C₄
prime radical	#41×C₃₅₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₅₉ ◁ C₂×C₄×C₃₅₉ ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5026 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#104×D₃₅₉, #37526458, #37526557, …
maximal subgroup of	C₂×#104×C₃₅₉, #421×C₃₅₉, #443×C₃₅₉, …
maximal normal subgroup of	C₂×#104×C₃₅₉, #421×C₃₅₉, #443×C₃₅₉, …
maximal quotient of	D₄⋊C₈×C₃₅₉, Q₈⋊C₈×C₃₅₉, #327×C₃₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11488, 11);