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#108×C₂₃₉ #21439829

order	7648
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₂₃₉ · Schur multiplier (H₂) = C₁

Aliases

#108×C₂₃₉

Subgroups

	subgroup	G/H
center	C₄×C₂₃₉	D₄
commutator	C₄	C₂×C₄×C₂₃₉
Frattini, cosocle	C₂×C₄	C₂²×C₂₃₉
socle	C₂×C₂₃₉	C₄⋊C₄
prime radical	C₂²×C₂₃₉	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃₉ ◁ C₂×C₄×C₂₃₉ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3346 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#29504578, #29504584, #29504587, …
maximal subgroup of	#359×C₂₃₉, #361×C₂₃₉, #362×C₂₃₉, …
maximal normal subgroup of	#359×C₂₃₉, #361×C₂₃₉, #362×C₂₃₉, …
maximal quotient of	#334×C₂₃₉, #335×C₂₃₉, #341×C₂₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7648, 15);