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C₄⋊C₁₆×C₁₃₇ #22576898

order	8768
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₄⋊C₁₆×C₁₃₇
unambiguous semidirect product	C₄⋊(C₁₆×C₁₃₇)

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₃₇	C₂²
commutator	C₂	C₂×C₁₆×C₁₃₇
Frattini, cosocle	C₂×C₈	C₂²×C₁₃₇
socle, prime radical	C₂²×C₁₃₇	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₇ ◁ G

50 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5480 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31778743, #31778746, #31778767, …
maximal subgroup of	D₄⋊C₁₆×C₁₃₇, #1330×C₁₃₇, Q₈⋊C₁₆×C₁₃₇, …
maximal normal subgroup of	D₄⋊C₁₆×C₁₃₇, #1330×C₁₃₇, Q₈⋊C₁₆×C₁₃₇, …
maximal quotient of	#1367×C₁₃₇, #1370×C₁₃₇, #1374×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 44);