C₂×C₅×C₂₃×D₂₉ #27211130

order	13340
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×C₂₃×D₂₉
unambiguous semidirect product	C₂₉⋊(C₂²×C₅×C₂₃)
unambiguous semidirect product	(C₂×C₂₉)⋊(C₂×C₅×C₂₃)

Splittings

Fitting, socle	C₂×C₅×C₂₃×C₂₉ ⋊ C₂
derived, Sylow	C₂₉ ⋊ C₂²×C₅×C₂₃
Hall	C₅×C₂₃×C₂₉ ⋊ C₂²
Hall	C₂₃×C₂₉ ⋊ C₂²×C₅
Hall	C₅×C₂₉ ⋊ C₂²×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₂₃	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂²×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₂₃×C₂₉	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₅×C₂₃

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 6670

A minimal faithful permutation representation — 2 generators on 59 points:

(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)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)(53,54,55,56,57);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(58,59)

Conjugacy classes & character table

3680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13340, 35);

C2×C5×C23×D29 #27211130