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C₈×Q₈×C₁₉₁ #27132240

order	12224
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉₁ · Schur multiplier (H₂) = C₂²

Aliases

C₈×Q₈×C₁₉₁

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉₁	C₂²
commutator	C₂	C₂²×C₈×C₁₉₁
Frattini, cosocle	C₂×C₄	C₂³×C₁₉₁
socle, prime radical	C₂²×C₁₉₁	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉₁ ◁ G

102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7640 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37570499, C₈×#15690274, C₈×#15690277, …
maximal subgroup of	Q₈⋊C₁₆×C₁₉₁, C₈×SD₁₆×C₁₉₁, C₈×Q₁₆×C₁₉₁, …
maximal normal subgroup of	Q₈⋊C₁₆×C₁₉₁, C₈×SD₁₆×C₁₉₁, C₈×Q₁₆×C₁₉₁, …
maximal quotient of	C₈×C₄⋊C₄×C₁₉₁, #1916×C₁₉₁, #1939×C₁₉₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12224, 126);