C₅×Dic₅₂ #11760111

order	1040
isoclinism	isoclinic class of #6095
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×Dic₅₂

Splittings

Hall	C₅×C₁₃ ⋊ Q₁₆
Sylow	C₁₃ ⋊ C₅×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₅	D₅₂
commutator, cosocle	C₄×C₁₃	C₂²×C₅
Frattini	C₄	C₂×C₅×D₁₃
Fitting	C₅×C₈×C₁₃	C₂
socle, prime radical	C₂×C₅×C₁₃	D₄
hypercenter	C₅×C₈	D₁₃
hypocenter	C₁₃	C₅×Q₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 1040

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13)(14,21,20,19,18,17,16,15)(22,23,24,25,26,27,28,29,30,31,32,33,34);(6,14,10,18)(7,15,11,19)(8,16,12,20)(9,17,13,21)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1040, 40);

C5×Dic52 #11760111