C₇×D₉×C₁₉ #14558795

order	2394
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₉×C₁₉
unambiguous semidirect product	C₉⋊(C₂×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₇×C₁₉
Frattini	C₃	D₃×C₇×C₁₉
Fitting	C₇×C₉×C₁₉	C₂
socle	C₃×C₇×C₁₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₇×C₁₉

24 conjugacy classes of subgroups.

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);(9,16)(10,15)(11,14)(12,13)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2394, 21);