C₇×C₁₇×D₁₉ #17985283

order	4522
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₇×D₁₉
unambiguous semidirect product	C₁₉⋊(C₂×C₇×C₁₇)

Splittings

Fitting, socle, Hall	C₇×C₁₇×C₁₉ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₇×C₁₇
Hall	C₁₇×C₁₉ ⋊ C₂×C₇
Hall	C₇×C₁₉ ⋊ C₂×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₁₇	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₇×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₇×C₁₇

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2261

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)

Conjugacy classes & character table

1309 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₇×C₁₇×D₁₉, C₇×C₁₇×D₅₇, C₇×C₁₇×D₁₉⋊C₃, …
maximal normal subgroup of	C₃×C₇×C₁₇×D₁₉, C₇×C₁₇×D₁₉⋊C₃, C₁₇×ΓL(1,𝔽₈)×D₁₉, …
maximal quotient of	C₃×C₇×C₁₇×D₁₉, C₇×C₁₇×D₅₇, C₅×C₇×C₁₇×D₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4522, 2);

C7×C17×D19 #17985283