Finite Group Databasebeta

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C₂×C₄×#14523248 #30651910

order	16256
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×C₄×#14523248

Splittings

Fitting	C₂²×C₄²×C₁₂₇ ⋊ C₂
Sylow	C₁₂₇ ⋊ C₂×C₄×#41

Subgroups

	subgroup	G/H
center	C₂×C₄²	C₂×D₁₂₇
commutator	C₂×C₁₂₇	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₁₂₇
Fitting	C₂²×C₄²×C₁₂₇	C₂
socle	C₂³×C₁₂₇	C₂⁴
prime radical	C₂²×#14523248	C₂
cosocle	C₂²×C₁₂₇	C₂⁵
hypercenter	C₂²×C₄²	D₁₂₇
hypocenter	C₁₂₇	C₂×C₄×#41
LCS	G ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₄² ◁ C₂²×C₄²

1728 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 17690);