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C₈×Q₈×C₁₇₃ #26011068

order	11072
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇₃ · Schur multiplier (H₂) = C₂²

Aliases

C₈×Q₈×C₁₇₃

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₇₃	C₂²
commutator	C₂	C₂²×C₈×C₁₇₃
Frattini, cosocle	C₂×C₄	C₂³×C₁₇₃
socle, prime radical	C₂²×C₁₇₃	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇₃ ◁ G

102 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	Q₈⋊#14583801, C₈×#14583813, C₈×#14583816, …
maximal subgroup of	Q₈⋊C₁₆×C₁₇₃, C₈×SD₁₆×C₁₇₃, C₈×Q₁₆×C₁₇₃, …
maximal normal subgroup of	Q₈⋊C₁₆×C₁₇₃, C₈×SD₁₆×C₁₇₃, C₈×Q₁₆×C₁₇₃, …
maximal quotient of	C₈×C₄⋊C₄×C₁₇₃, #1916×C₁₇₃, #1939×C₁₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11072, 126);