Finite Group Databasebeta

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C₃×Dic₃×C₉₈₃ #47978151

order	35388
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₉₈₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×Dic₃×C₉₈₃
unambiguous semidirect product	C₃⋊(C₃×C₄×C₉₈₃)

Splittings

derived	C₃ ⋊ C₃×C₄×C₉₈₃
Hall	C₃²×C₉₈₃ ⋊ C₄
Sylow	C₃² ⋊ C₄×C₉₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₉₈₃	D₃
commutator, hypocenter	C₃	C₃×C₄×C₉₈₃
Frattini	C₂	C₃×D₃×C₉₈₃
Fitting, socle, prime radical	C₂×C₃²×C₉₈₃	C₂
cosocle	C₂×C₃	C₂×C₃×C₉₈₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₉₈₃

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11796

Conjugacy classes & character table

17694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35388, 15);