C₅×D₇×C₂₉ #14523199

order	2030
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₇×C₂₉
unambiguous semidirect product	C₇⋊(C₂×C₅×C₂₉)

	subgroup	G/H
center, hypercenter	C₅×C₂₉	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₂₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₂₉

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1015

A minimal faithful permutation representation — 2 generators on 41 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);(7,12)(8,11)(9,10)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2030, 4);