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C₄⋊C₈×D₁₆₇ #24923288

order	10688
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₄⋊C₈×D₁₆₇

Splittings

Fitting	C₄⋊C₈×C₁₆₇ ⋊ C₂
Sylow	C₁₆₇ ⋊ C₂×C₄⋊C₈

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₆₇
commutator	C₂×C₁₆₇	C₂²×C₈
Fitting	C₄⋊C₈×C₁₆₇	C₂
socle	C₂²×C₁₆₇	C₂²×C₄
prime radical	C₂²×D₁₆₇	C₂×C₄
cosocle	C₂×C₄×C₁₆₇	C₂³
hypercenter	C₄⋊C₈	D₁₆₇
hypocenter	C₁₆₇	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₁₆₇ ▷ C₁₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

138 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₄⋊C₈×D₁₆₇, Q₈⋊C₈×D₁₆₇, #36322522, …
maximal normal subgroup of	D₄⋊C₈×D₁₆₇, Q₈⋊C₈×D₁₆₇, #36322522, …
maximal quotient of	#334×D₁₆₇, #335×D₁₆₇, #36322883, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 568);