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C₂×H(3,𝔽₄)×D₄₃ #26003468

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹¹×C₄²

Aliases

C₂×H(3,𝔽₄)×D₄₃

Splittings

Fitting	C₂×C₄₃×H(3,𝔽₄) ⋊ C₂
Sylow	C₄₃ ⋊ C₂²×H(3,𝔽₄)

Subgroups

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄₃×H(3,𝔽₄)	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂×H(3,𝔽₄)	D₄₃
hypocenter	C₄₃	C₂²×H(3,𝔽₄)
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×H(3,𝔽₄)

10246 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076439);