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C₁₇×(C₇⋊C₉)⋊Dic₇ #44472501

order	29988
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×(C₇⋊C₉)⋊Dic₇
unambiguous semidirect product	(C₇⋊C₉)⋊(C₁₇×Dic₇)

Splittings

derived, Sylow	C₇² ⋊ C₄×C₉×C₁₇
Hall	C₇×C₁₇×C₇⋊C₉ ⋊ C₄
Hall	C₁₇×C₇⋊Dic₇ ⋊ C₉
Hall	C₇²×C₁₇ ⋊ C₄×C₉
Hall	C₇×C₇⋊C₉ ⋊ C₄×C₁₇
Hall	C₇⋊Dic₇ ⋊ C₉×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇	ΓL(1,𝔽₈)⋊D₇
commutator, hypocenter	C₇²	C₄×C₉×C₁₇
Frattini	C₂×C₃	C₁₇×ΓL(1,𝔽₈)⋊D₇
Fitting, socle, prime radical	C₂×C₃×C₇²×C₁₇	C₂×C₃
cosocle	C₂×C₃×C₇²	C₂×C₃×C₁₇
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃×C₁₇

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4284

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 142);