C₃×C₅×Dic₂₆ #13095672

order	1560
isoclinism	isoclinic class of Dic₂₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₅×Dic₂₆

Splittings

Hall	C₃×C₅×C₁₃ ⋊ Q₈
Hall	C₅×C₁₃ ⋊ C₃×Q₈
Hall	C₃×C₁₃ ⋊ C₅×Q₈
Sylow	C₁₃ ⋊ C₃×C₅×Q₈

Subgroups

	subgroup	G/H
center	C₂×C₃×C₅	C₂×D₁₃
commutator, cosocle	C₂×C₁₃	C₂²×C₃×C₅
Frattini	C₂	C₂×C₃×C₅×D₁₃
Fitting	C₃×C₄×C₅×C₁₃	C₂
socle, prime radical	C₂×C₃×C₅×C₁₃	C₂²
hypercenter	C₃×C₄×C₅	D₁₃
hypocenter	C₁₃	C₃×C₅×Q₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₃×C₄×C₅

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1560

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1560, 108);

C3×C5×Dic26 #13095672