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D₃×C₄₉×C₈₉ #39908577

order	26166
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₉×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₄₉×C₈₉
unambiguous semidirect product	C₃⋊(C₂×C₄₉×C₈₉)

Splittings

Fitting, Hall	C₃×C₄₉×C₈₉ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₄₉×C₈₉
Hall	C₃×C₈₉ ⋊ C₂×C₄₉
Hall	C₃×C₄₉ ⋊ C₂×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₄₉×C₈₉	D₃
commutator, hypocenter	C₃	C₂×C₄₉×C₈₉
Frattini	C₇	D₃×C₇×C₈₉
Fitting	C₃×C₄₉×C₈₉	C₂
socle	C₃×C₇×C₈₉	C₂×C₇
prime radical	D₃×C₇×C₈₉	C₇
cosocle	C₃×C₇	C₂×C₇×C₈₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₄₉×C₈₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 13083

Conjugacy classes & character table

13083 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26166, 6);