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C₄×M₁₆×C₁₇₃ #26011027

order	11072
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₇₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

C₄×M₁₆×C₁₇₃

Subgroups

	subgroup	G/H
center	C₄²×C₁₇₃	C₂²
commutator	C₂	C₂×C₄²×C₁₇₃
Frattini, cosocle	C₂×C₄	C₂³×C₁₇₃
socle	C₂²×C₁₇₃	C₂²×C₄
prime radical	C₂³×C₁₇₃	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₇₃ ◁ G

142 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6920 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36351401, #36351414, #36351428, …
maximal subgroup of	#1278×C₁₇₃, #1283×C₁₇₃, #1288×C₁₇₃, …
maximal normal subgroup of	#1278×C₁₇₃, #1283×C₁₇₃, #1288×C₁₇₃, …
maximal quotient of	C₈×M₁₆×C₁₇₃, #1451×C₁₇₃, #1453×C₁₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11072, 85);