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C₂×C₄×Q₈×C₁₃₇ #22577051

order	8768
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₄×Q₈×C₁₃₇

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂²
commutator	C₂	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²	C₂⁴×C₁₃₇
socle, prime radical	C₂³×C₁₃₇	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₇ ◁ G

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5480 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31779113, #31779133, C₂×Q₈⋊#11764040, …
maximal subgroup of	#1461×C₁₃₇, #1467×C₁₃₇, C₂×Q₈⋊C₈×C₁₃₇, …
maximal normal subgroup of	#1461×C₁₃₇, #1467×C₁₃₇, C₂×Q₈⋊C₈×C₁₃₇, …
maximal quotient of	C₂×C₄×C₄⋊C₄×C₁₃₇, C₄²×Q₈×C₁₃₇, C₂×#387×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 197);