Finite Group Databasebeta

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C₂×C₃⋊D₃×C₂₈₉ #23780825

order	10404
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₈₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃⋊D₃×C₂₈₉
unambiguous semidirect product	(C₂×C₃)⋊(D₃×C₂₈₉)

Splittings

Fitting	C₂×C₃²×C₂₈₉ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂²×C₂₈₉
Hall	C₃²×C₂₈₉ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₈₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₂²×C₂₈₉
Frattini	C₁₇	C₂×C₁₇×C₃⋊D₃
Fitting	C₂×C₃²×C₂₈₉	C₂
socle	C₂×C₃²×C₁₇	C₂×C₁₇
prime radical	C₂×C₁₇×C₃⋊D₃	C₁₇
cosocle	C₃²×C₁₇	C₂²×C₁₇
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₂₈₉

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10404, 35);