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D₇⋊C₉×C₁₇₃ #36345461

order	21798
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇⋊C₉×C₁₇₃
unambiguous semidirect product	D₇⋊(C₉×C₁₇₃)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₁₇₃)
unambiguous semidirect product	(D₇×C₁₇₃)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₁₇₃
Hall	C₇⋊C₉×C₁₇₃ ⋊ C₂
Hall	D₇×C₁₇₃ ⋊ C₉
Hall	C₇×C₁₇₃ ⋊ C₂×C₉
Hall	C₇⋊C₉ ⋊ C₂×C₁₇₃
Hall	D₇ ⋊ C₉×C₁₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇₃	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₁₇₃
Frattini	C₃	AGL(1,𝔽₇)×C₁₇₃
Fitting, socle	C₃×C₇×C₁₇₃	C₂×C₃
prime radical	C₃×D₇×C₁₇₃	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₇₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₇₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10899

Conjugacy classes & character table

3633 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21798, 11);