Finite Group Databasebeta

← Prev (#37590768) Next (#37590770) →

C₁₃×C₁₉×#1035 #37590769

order	24700
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₃×C₁₉×#1035

Splittings

Fitting, Hall	C₁₃×C₁₉×C₂₅ ⋊ C₄
derived, Sylow	C₂₅ ⋊ C₄×C₁₃×C₁₉
Hall	C₁₉×C₂₅ ⋊ C₄×C₁₃
Hall	C₁₃×C₂₅ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	#1035
commutator, hypocenter	C₂₅	C₄×C₁₃×C₁₉
Frattini	C₅	C₁₃×C₁₉×AGL(1,𝔽₅)
Fitting	C₁₃×C₁₉×C₂₅	C₄
socle	C₅×C₁₃×C₁₉	AGL(1,𝔽₅)
prime radical	C₁₃×C₁₉×D₂₅	C₂
cosocle	D₂₅	C₂×C₁₃×C₁₉
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₁₃×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 6175

Conjugacy classes & character table

2470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24700, 13);