C₇×C₉×D₁₉ #14558792

order	2394
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇×C₉×D₁₉

Splittings

Fitting, Hall	C₇×C₉×C₁₉ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₇×C₉
Hall	C₉×C₁₉ ⋊ C₂×C₇
Hall	C₇×C₁₉ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉	D₁₉
commutator, hypocenter	C₁₉	C₂×C₇×C₉
Frattini	C₃	C₃×C₇×D₁₉
Fitting	C₇×C₉×C₁₉	C₂
socle	C₃×C₇×C₁₉	C₂×C₃
prime radical	C₃×C₇×D₁₉	C₃
cosocle	C₃×C₁₉	C₂×C₃×C₇
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₇×C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1197

A minimal faithful permutation representation — 2 generators on 35 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);(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×D₇×D₁₉, C₇×D₉×D₁₉, D₁₉×D₆₃, …
maximal normal subgroup of	C₉×D₇×D₁₉, C₇×D₉×D₁₉, D₁₉×D₆₃, …
maximal quotient of	C₇×C₉×Dic₁₉, C₂×C₇×C₉×D₁₉, C₅×C₇×C₉×D₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2394, 18);

C7×C9×D19 #14558792