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C₃×D₉₇₁ #19154190

order	5826
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₉₇₁
unambiguous semidirect product	C₉₇₁⋊(C₂×C₃)

Splittings

Fitting, socle, Hall	C₃×C₉₇₁ ⋊ C₂
derived, Sylow	C₉₇₁ ⋊ C₂×C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₉₇₁
commutator, hypocenter	C₉₇₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₉₇₁	C₂
LCS	G ▷ C₉₇₁
UCS	C₁ ◁ C₃

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1461 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×D₉₇₁, C₂×C₃×D₉₇₁, C₉×D₉₇₁, …
maximal normal subgroup of	D₃×D₉₇₁, C₂×C₃×D₉₇₁, C₉×D₉₇₁, …
maximal quotient of	C₃×Dic₉₇₁, C₂×C₃×D₉₇₁, C₉×D₉₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5826, 2);