Finite Group Databasebeta

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#346×Dic₄₃ #25011417

order	11008
automorphism	?
homology	Abelianization (H₁) = C₄²×C₈ · Schur multiplier (H₂) = C₂×C₄²

Aliases

#346×Dic₄₃

Splittings

C₄₃ ⋊ C₄×#346

Subgroups

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₄₃
commutator	C₂×C₄₃	C₄²×C₈
Fitting	C₂×C₄₃×#346	C₂
socle, prime radical	C₂³×C₄₃	C₂²×C₈
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#346	D₄₃
hypocenter	C₄₃	C₄×#346
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×#346

510 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 84388);