D₁₉×C₇⋊C₉ #14558779

order	2394
isoclinism	isoclinic class of ΓL(1,𝔽₈)×D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

D₁₉×C₇⋊C₉

Splittings

derived, Hall	C₇×C₁₉ ⋊ C₂×C₉
Hall	C₁₉×C₇⋊C₉ ⋊ C₂
Hall	C₇×D₁₉ ⋊ C₉
Sylow	C₁₉ ⋊ C₂×C₇⋊C₉
Sylow	C₇ ⋊ C₉×D₁₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	ΓL(1,𝔽₈)×D₁₉
commutator, hypocenter	C₇×C₁₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₇×C₁₉	C₂×C₃
prime radical	C₃×C₇×D₁₉	C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₃

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

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2394, 5);

D19×C7⋊C9 #14558779

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

D₁₉×C₇⋊C₉ #14558779