C₂₉×D₂₁ #11927397

order	1218
isoclinism	isoclinic class of D₂₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×D₂₁
unambiguous semidirect product	C₃⋊(D₇×C₂₉)
unambiguous semidirect product	C₇⋊(D₃×C₂₉)

	subgroup	G/H
center, hypercenter	C₂₉	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₂₉	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂₉

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 609

A minimal faithful permutation representation — 2 generators on 39 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);(31,32)(34,39)(35,38)(36,37)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1218, 14);