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C₂²×C₅²⋊#4294 #30685613

order	17100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂²×C₅²⋊#4294

Splittings

derived, Hall	C₅²×C₁₉ ⋊ C₂²×C₉
Hall	C₂²×C₅²×C₁₉ ⋊ C₉
Hall	C₂²×C₅² ⋊ #4294
Hall	C₂²×C₁₉ ⋊ C₅²⋊C₉
Sylow	C₅² ⋊ C₂²×#4294
Sylow	C₁₉ ⋊ C₂²×C₅²⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃	C₁₉⋊(C₅²⋊C₃)
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Frattini	C₃	C₂²×C₁₉⋊(C₅²⋊C₃)
Fitting, socle, prime radical	C₂²×C₃×C₅²×C₁₉	C₃
cosocle	C₃×C₅²×C₁₉	C₂²×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂²×C₃

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3420

Conjugacy classes & character table

1932 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 250);