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C₂×C₄×Q₈×C₁₄₉ #23749273

order	9536
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₄₉ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₄×Q₈×C₁₄₉

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₄₉	C₂²
commutator	C₂	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂²	C₂⁴×C₁₄₉
socle, prime radical	C₂³×C₁₄₉	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₄₉ ◁ G

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5960 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#34043015, #34043035, C₂×Q₈⋊#11924746, …
maximal subgroup of	#1461×C₁₄₉, #1467×C₁₄₉, C₂×Q₈⋊C₈×C₁₄₉, …
maximal normal subgroup of	#1461×C₁₄₉, #1467×C₁₄₉, C₂×Q₈⋊C₈×C₁₄₉, …
maximal quotient of	C₂×C₄×C₄⋊C₄×C₁₄₉, C₄²×Q₈×C₁₄₉, C₂×#387×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 197);