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D₃×D₇×C₂₈₉ #37566174

order	24276
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₈₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₇×C₂₈₉
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₂₈₉)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₂₈₉)
unambiguous semidirect product	D₂₁⋊(C₂×C₂₈₉)

Splittings

Fitting, Hall	C₃×C₇×C₂₈₉ ⋊ C₂²
derived, Hall	C₃×C₇ ⋊ C₂²×C₂₈₉
Hall	C₇×C₂₈₉ ⋊ C₂×D₃
Hall	C₃×C₂₈₉ ⋊ C₂×D₇
Sylow	C₇ ⋊ C₂×D₃×C₂₈₉
Sylow	C₃ ⋊ C₂×D₇×C₂₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₈₉	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₂₈₉
Frattini	C₁₇	D₃×D₇×C₁₇
Fitting	C₃×C₇×C₂₈₉	C₂²
socle, cosocle	C₃×C₇×C₁₇	C₂²×C₁₇
prime radical	D₃×D₇×C₁₇	C₁₇
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂₈₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 6069

Conjugacy classes & character table

4335 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24276, 27);