C₂₉×D₄₁ #14558646

order	2378
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×D₄₁
unambiguous semidirect product	C₄₁⋊(C₂×C₂₉)

Splittings

Fitting, socle, Hall	C₂₉×C₄₁ ⋊ C₂
derived, Sylow	C₄₁ ⋊ C₂×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₂₉×C₄₁	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 70
transitive degree	μ_t(G) = 1189

A minimal faithful permutation representation — 2 generators on 70 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)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70);(31,70)(32,69)(33,68)(34,67)(35,66)(36,65)(37,64)(38,63)(39,62)(40,61)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#4223, #18011703, D₂₉×D₄₁, …
maximal normal subgroup of	C₂₉×#4223, #18011703, D₂₉×D₄₁, …
maximal quotient of	C₂₉×Dic₄₁, C₂×C₂₉×D₄₁, C₅×C₂₉×D₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2378, 2);

C29×D41 #14558646