Finite Group Databasebeta

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C₄×#14583410 #25255060

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

C₄×#14583410

Splittings

Fitting	C₂³×C₄²×C₄₃ ⋊ C₂
Sylow	C₄₃ ⋊ C₄×#525

Subgroups

	subgroup	G/H
center	C₂×C₄²	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₃
Fitting	C₂³×C₄²×C₄₃	C₂
socle, cosocle	C₂³×C₄₃	C₂⁵
prime radical	C₂×#14583410	C₂
hypercenter	C₂³×C₄²	D₄₃
hypocenter	C₄₃	C₄×#525
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂³×C₄²

3902 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328031);