D₅×C₁₇×C₂₃ #16840935

order	3910
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅×C₁₇×C₂₃
unambiguous semidirect product	C₅⋊(C₂×C₁₇×C₂₃)

	subgroup	G/H
center, hypercenter	C₁₇×C₂₃	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₁₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₂₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₇×C₂₃

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1955

A minimal faithful permutation representation — 2 generators on 45 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(2,5)(3,4)

1564 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3910, 5);