C₇×C₁₉×D₁₇ #17985284

order	4522
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₉×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×C₇×C₁₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₇×C₁₉	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₇×C₁₉

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);(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₇×C₁₉×D₁₇, C₇×C₁₉×D₅₁, C₇×D₁₇×C₁₉⋊C₃, …
maximal normal subgroup of	C₃×C₇×C₁₉×D₁₇, C₇×D₁₇×C₁₉⋊C₃, C₁₉×ΓL(1,𝔽₈)×D₁₇, …
maximal quotient of	C₃×C₇×C₁₉×D₁₇, C₇×C₁₉×D₅₁, C₅×C₇×C₁₉×D₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4522, 3);

C7×C19×D17 #17985284