Dic₅×C₂₃×C₂₉ #27211100

order	13340
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₃×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

Dic₅×C₂₃×C₂₉

Splittings

derived, Sylow	C₅ ⋊ C₄×C₂₃×C₂₉
Hall	C₅×C₂₃×C₂₉ ⋊ C₄
Hall	C₅×C₂₉ ⋊ C₄×C₂₃
Hall	C₅×C₂₃ ⋊ C₄×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₃×C₂₉	D₅
commutator, hypocenter	C₅	C₄×C₂₃×C₂₉
Frattini	C₂	D₅×C₂₃×C₂₉
Fitting, socle, prime radical	C₂×C₅×C₂₃×C₂₉	C₂
cosocle	C₂×C₅	C₂×C₂₃×C₂₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₂₃×C₂₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 13340

A minimal faithful permutation representation — 2 generators on 61 points:

(2,3)(4,5)(6,9,8,7)(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)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61);(1,2,4,5,3)

Conjugacy classes & character table

5336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13340, 5);

Dic5×C23×C29 #27211100