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D₇⋊C₉×C₁₅₇ #34089947

order	19782
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₅₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇⋊C₉×C₁₅₇
unambiguous semidirect product	D₇⋊(C₉×C₁₅₇)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₁₅₇)

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₁₅₇
Hall	C₇⋊C₉×C₁₅₇ ⋊ C₂
Hall	D₇×C₁₅₇ ⋊ C₉
Hall	C₇×C₁₅₇ ⋊ C₂×C₉
Hall	C₇⋊C₉ ⋊ C₂×C₁₅₇
Hall	D₇ ⋊ C₉×C₁₅₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₅₇	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₁₅₇
Frattini	C₃	AGL(1,𝔽₇)×C₁₅₇
Fitting, socle	C₃×C₇×C₁₅₇	C₂×C₃
prime radical	C₃×D₇×C₁₅₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₅₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₅₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9891

Conjugacy classes & character table

3297 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19782, 18);