Finite Group Databasebeta

← Prev (#30685644) Next (#30685646) →

C₄×C₁₉⋊C₃×C₅²⋊C₃ #30685645

order	17100
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product	C₄×C₁₉⋊C₃×C₅²⋊C₃
unambiguous semidirect product	(C₄×C₅²×C₁₉⋊C₃)⋊C₃
unambiguous semidirect product	(C₄×C₁₉×C₅²⋊C₃)⋊C₃
unambiguous semidirect product	(C₄×C₁₉⋊(C₅²⋊C₃))⋊C₃

Splittings

Fitting, Hall	C₄×C₅²×C₁₉ ⋊ C₃²
derived, Hall	C₅²×C₁₉ ⋊ C₃²×C₄
Hall	C₄×C₅² ⋊ C₃×C₁₉⋊C₃
Hall	C₄×C₁₉ ⋊ C₃×C₅²⋊C₃
Sylow	C₅² ⋊ C₃×C₄×C₁₉⋊C₃
Sylow	C₁₉ ⋊ C₃×C₄×C₅²⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄	C₁₉⋊C₃×C₅²⋊C₃
commutator, hypocenter	C₅²×C₁₉	C₃²×C₄
Frattini	C₂	C₂×C₁₉⋊C₃×C₅²⋊C₃
Fitting	C₄×C₅²×C₁₉	C₃²
socle, cosocle	C₂×C₅²×C₁₉	C₂×C₃²
prime radical	C₂×C₁₉⋊C₃×C₅²⋊C₃	C₂
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₄

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1140

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 282);