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#433×C₁₃₉ #22580518

order	8896
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃₉ · Schur multiplier (H₂) = C₄

Aliases

#433×C₁₃₉

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃₉	C₂³
commutator	C₂²	C₂²×C₄×C₁₃₉
Frattini, cosocle	C₂×C₄	C₂³×C₁₃₉
socle	C₂²×C₁₃₉	C₂²×C₄
prime radical	C₂³×C₁₃₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₉ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3892 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#433×D₁₃₉, #31815038, #31815045, …
maximal subgroup of	C₂×#433×C₁₃₉, #2921×C₁₃₉, #2922×C₁₃₉, …
maximal normal subgroup of	C₂×#433×C₁₃₉, #2921×C₁₃₉, #2922×C₁₃₉, …
maximal quotient of	#1746×C₁₃₉, #1750×C₁₃₉, #1768×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 114);