Finite Group Databasebeta

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#568×C₁₇₃ #26011191

order	11072
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇₃ · Schur multiplier (H₂) = C₂⁵

Aliases

#568×C₁₇₃

Subgroups

	subgroup	G/H
center	C₄×C₁₇₃	C₂⁴
commutator	C₂	C₂³×C₄×C₁₇₃
Frattini, cosocle	C₄	C₂⁴×C₁₇₃
socle	C₂×C₁₇₃	C₂³×C₄
prime radical	C₂×#41×C₁₇₃	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇₃ ◁ G

258 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5882 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36353783, #36353803, #36353849, …
maximal subgroup of	#1858×C₁₇₃, #1861×C₁₇₃, #1868×C₁₇₃, …
maximal normal subgroup of	#1858×C₁₇₃, #1861×C₁₇₃, #1868×C₁₇₃, …
maximal quotient of	#2873×C₁₇₃, #2875×C₁₇₃, #2879×C₁₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11072, 249);