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C₂×C₁₉×D₁₁×C₂₅ #35229853

order	20900
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉×C₂₅ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₁₉×D₁₁×C₂₅

Splittings

Fitting	C₂×C₁₁×C₁₉×C₂₅ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂²×C₁₉×C₂₅
Hall	C₁₁×C₁₉×C₂₅ ⋊ C₂²
Hall	C₁₁×C₂₅ ⋊ C₂²×C₁₉
Hall	C₁₁×C₁₉ ⋊ C₂²×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₂₅	D₁₁
commutator, hypocenter	C₁₁	C₂²×C₁₉×C₂₅
Frattini	C₅	C₂×C₅×C₁₉×D₁₁
Fitting	C₂×C₁₁×C₁₉×C₂₅	C₂
socle	C₂×C₅×C₁₁×C₁₉	C₂×C₅
prime radical	C₂×C₅×C₁₉×D₁₁	C₅
cosocle	C₅×C₁₁	C₂²×C₅×C₁₉
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₉×C₂₅

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10450

Conjugacy classes & character table

6650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 35);