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C₈×Q₈×C₁₉₃ #27134836

order	12352
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉₃ · Schur multiplier (H₂) = C₂²

Aliases

C₈×Q₈×C₁₉₃

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉₃	C₂²
commutator	C₂	C₂²×C₈×C₁₉₃
Frattini, cosocle	C₂×C₄	C₂³×C₁₉₃
socle, prime radical	C₂²×C₁₉₃	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉₃ ◁ G

102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Q₈⋊C₁₆×C₁₉₃, C₈×SD₁₆×C₁₉₃, C₈×Q₁₆×C₁₉₃, …
maximal normal subgroup of	Q₈⋊C₁₆×C₁₉₃, C₈×SD₁₆×C₁₉₃, C₈×Q₁₆×C₁₉₃, …
maximal quotient of	C₈×C₄⋊C₄×C₁₉₃, #1916×C₁₉₃, #1939×C₁₉₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 126);