C₇×D₅×C₂₉ #14523201

order	2030
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₅×C₂₉
unambiguous semidirect product	C₅⋊(C₂×C₇×C₂₉)

	subgroup	G/H
center, hypercenter	C₇×C₂₉	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₇×C₂₉
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₂₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₇×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);(9,12)(10,11)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2030, 6);