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D₄₃×D₄⋊C₁₆ #25006294

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂⁴

Aliases

D₄₃×D₄⋊C₁₆

Splittings

Fitting	C₄₃×D₄⋊C₁₆ ⋊ C₂
Sylow	C₄₃ ⋊ C₂×D₄⋊C₁₆

Subgroups

	subgroup	G/H
center	C₂×C₈	D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₁₆
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₄₃×D₄⋊C₁₆	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₈
prime radical	C₂×D₄×D₄₃	C₈
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	D₄⋊C₁₆	D₄₃
hypocenter	C₄₃	C₂×D₄⋊C₁₆
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ D₄⋊C₁₆

470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 79265);