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C₁₉×C₂₅×Dic₁₃ #37590759

order	24700
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

C₁₉×C₂₅×Dic₁₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₂₅	D₁₃
commutator, hypocenter	C₁₃	C₄×C₁₉×C₂₅
Frattini	C₂×C₅	C₅×C₁₉×D₁₃
Fitting	C₂×C₁₃×C₁₉×C₂₅	C₂
socle, prime radical	C₂×C₅×C₁₃×C₁₉	C₂×C₅
cosocle	C₂×C₅×C₁₃	C₂×C₅×C₁₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₉×C₂₅

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 24700

Conjugacy classes & character table

7600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24700, 3);