Finite Group Databasebeta

← Prev (#26374740) Next (#26374742) →

C₄×#15689634 #26374741

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

C₄×#15689634

Splittings

Fitting	C₂³×C₄²×C₄₇ ⋊ C₂
Sylow	C₄₇ ⋊ C₄×#525

Subgroups

	subgroup	G/H
center	C₂×C₄²	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂³×C₄²×C₄₇	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂×#15689634	C₂
hypercenter	C₂³×C₄²	D₄₇
hypocenter	C₄₇	C₄×#525
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₂³×C₄²

3902 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328031);