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C₂×C₄×Q₈×C₁₆₇ #24922917

order	10688
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₆₇ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₄×Q₈×C₁₆₇

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₆₇	C₂²
commutator	C₂	C₂³×C₄×C₁₆₇
Frattini, cosocle	C₂²	C₂⁴×C₁₆₇
socle, prime radical	C₂³×C₁₆₇	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₆₇ ◁ G

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6680 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36322462, #36322482, C₂×Q₈⋊(C₁₆₇⋊C₈), …
maximal subgroup of	#1461×C₁₆₇, #1467×C₁₆₇, C₂×Q₈⋊C₈×C₁₆₇, …
maximal normal subgroup of	#1461×C₁₆₇, #1467×C₁₆₇, C₂×Q₈⋊C₈×C₁₆₇, …
maximal quotient of	C₂×C₄×C₄⋊C₄×C₁₆₇, C₄²×Q₈×C₁₆₇, C₂×#387×C₁₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 197);