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C₄×C₅²⋊#4294 #30685444

order	17100
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₄×C₅²⋊#4294
unambiguous semidirect product	(C₄×C₅²)⋊#4294

Splittings

derived, Hall	C₅²×C₁₉ ⋊ C₄×C₉
Hall	C₄×C₅²×C₁₉ ⋊ C₉
Hall	C₄×C₅² ⋊ #4294
Hall	C₄×C₁₉ ⋊ C₅²⋊C₉
Sylow	C₅² ⋊ C₄×#4294
Sylow	C₁₉ ⋊ C₄×C₅²⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄	C₁₉⋊(C₅²⋊C₃)
commutator, hypocenter	C₅²×C₁₉	C₄×C₉
Frattini	C₂×C₃	C₂×C₁₉⋊(C₅²⋊C₃)
Fitting	C₃×C₄×C₅²×C₁₉	C₃
socle, prime radical, cosocle	C₂×C₃×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₃×C₄

60 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, 81);