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#433×C₁₇₃ #26011056

order	11072
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇₃ · Schur multiplier (H₂) = C₄

Aliases

#433×C₁₇₃

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇₃	C₂³
commutator	C₂²	C₂²×C₄×C₁₇₃
Frattini, cosocle	C₂×C₄	C₂³×C₁₇₃
socle	C₂²×C₁₇₃	C₂²×C₄
prime radical	C₂³×C₁₇₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇₃ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4844 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#433×D₁₇₃, #36362197, #36362204, …
maximal subgroup of	C₂×#433×C₁₇₃, #2921×C₁₇₃, #2922×C₁₇₃, …
maximal normal subgroup of	C₂×#433×C₁₇₃, #2921×C₁₇₃, #2922×C₁₇₃, …
maximal quotient of	#1746×C₁₇₃, #1750×C₁₇₃, #1768×C₁₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11072, 114);