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C₂×D₅×C₁₉×C₄₉ #32916007

order	18620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉×C₄₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₅×C₁₉×C₄₉
unambiguous semidirect product	C₅⋊(C₂²×C₁₉×C₄₉)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₁₉×C₄₉)

Splittings

Fitting	C₂×C₅×C₁₉×C₄₉ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂²×C₁₉×C₄₉
Hall	C₅×C₁₉×C₄₉ ⋊ C₂²
Hall	C₅×C₄₉ ⋊ C₂²×C₁₉
Hall	C₅×C₁₉ ⋊ C₂²×C₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₄₉	D₅
commutator, hypocenter	C₅	C₂²×C₁₉×C₄₉
Frattini	C₇	C₂×C₇×D₅×C₁₉
Fitting	C₂×C₅×C₁₉×C₄₉	C₂
socle	C₂×C₅×C₇×C₁₉	C₂×C₇
prime radical	C₂×C₇×D₅×C₁₉	C₇
cosocle	C₅×C₇	C₂²×C₇×C₁₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₁₉×C₄₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9310

Conjugacy classes & character table

7448 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18620, 24);