Finite Group Databasebeta

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C₂×C₄₇⋊#1309 #26106691

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product	C₂×C₄₇⋊#1309
unambiguous semidirect product	(C₂×C₄₇)⋊#1309

Splittings

C₄₇ ⋊ C₂×#1309

Subgroups

	subgroup	G/H
center	C₂³	C₄₇⋊#95
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#423	C₂
socle	C₂³×C₄₇	#95
prime radical	C₂⁴×C₄₇	C₄²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#423	D₄₇
hypocenter	C₄₇	C₂×#1309
LCS	G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#423

658 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 59981);