C₂₉×D₃₅ #14523203

order	2030
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×D₃₅
unambiguous semidirect product	C₅⋊(D₇×C₂₉)
unambiguous semidirect product	C₇⋊(D₅×C₂₉)

Splittings

Fitting, socle, Hall	C₅×C₇×C₂₉ ⋊ C₂
derived, Hall	C₅×C₇ ⋊ C₂×C₂₉
Hall	C₇×C₂₉ ⋊ D₅
Hall	C₅×C₂₉ ⋊ D₇
Sylow	C₇ ⋊ D₅×C₂₉
Sylow	C₅ ⋊ D₇×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₂₉	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1015

A minimal faithful permutation representation — 2 generators on 41 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);(31,34)(32,33)(36,41)(37,40)(38,39)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₂₉×D₃₅, D₅×D₇×C₂₉, D₃₅⋊D₂₉, …
maximal normal subgroup of	D₂₉×D₃₅, D₅×D₇×C₂₉, D₃₅⋊D₂₉, …
maximal quotient of	C₂₉×Dic₃₅, C₂×C₂₉×D₃₅, C₂₉×D₂₄₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2030, 8);

C29×D35 #14523203