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C₂²⋊C₁₆×C₁₃₉ #22580433

order	8896
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₃₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂²⋊C₁₆×C₁₃₉
unambiguous semidirect product	C₂²⋊(C₁₆×C₁₃₉)

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₃₉	C₂²
commutator	C₂	C₂×C₁₆×C₁₃₉
Frattini, cosocle	C₂×C₈	C₂²×C₁₃₉
socle	C₂²×C₁₃₉	C₂×C₈
prime radical	C₂³×C₁₃₉	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₉ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5560 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31804327, #31804329, #31804343, …
maximal subgroup of	#1314×C₁₃₉, #1315×C₁₃₉, #1322×C₁₃₉, …
maximal normal subgroup of	#1314×C₁₃₉, #1315×C₁₃₉, #1322×C₁₃₉, …
maximal quotient of	#1314×C₁₃₉, #1322×C₁₃₉, D₄⋊C₁₆×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 29);