Finite Group Databasebeta

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C₁₃×C₁₉×Dic₂₅ #37590761

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

Aliases

C₁₃×C₁₉×Dic₂₅

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₁₉	D₂₅
commutator, hypocenter	C₂₅	C₄×C₁₃×C₁₉
Frattini	C₂×C₅	D₅×C₁₃×C₁₉
Fitting	C₂×C₁₃×C₁₉×C₂₅	C₂
socle, prime radical	C₂×C₅×C₁₃×C₁₉	D₅
cosocle	C₂×C₂₅	C₂×C₁₃×C₁₉
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₁₃×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 24700

Conjugacy classes & character table

6916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24700, 5);