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C₁₉×D₁₇×C₄₉ #44539601

order	31654
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₁₇×C₄₉
unambiguous semidirect product	C₁₇⋊(C₂×C₁₉×C₄₉)

Splittings

Fitting, Hall	C₁₇×C₁₉×C₄₉ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₁₉×C₄₉
Hall	C₁₇×C₄₉ ⋊ C₂×C₁₉
Hall	C₁₇×C₁₉ ⋊ C₂×C₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₄₉	D₁₇
commutator, hypocenter	C₁₇	C₂×C₁₉×C₄₉
Frattini	C₇	C₇×C₁₉×D₁₇
Fitting	C₁₇×C₁₉×C₄₉	C₂
socle	C₇×C₁₇×C₁₉	C₂×C₇
prime radical	C₇×C₁₉×D₁₇	C₇
cosocle	C₇×C₁₇	C₂×C₇×C₁₉
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₁₉×C₄₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15827

Conjugacy classes & character table

9310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31654, 3);