C₂×C₃×D₂₉ #66830

order	348
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×D₂₉
unambiguous semidirect product	C₂₉⋊(C₂²×C₃)
unambiguous semidirect product	(C₂×C₂₉)⋊(C₂×C₃)

Splittings

Fitting, socle	C₂×C₃×C₂₉ ⋊ C₂
derived, Sylow	C₂₉ ⋊ C₂²×C₃
Hall	C₃×C₂₉ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₂₉	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₃

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 174

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2)(3,4,5)(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);(1,2)(6,7,9,11,13,15,17,19,21,23,25,27,29,31,33,34,32,30,28,26,24,22,20,18,16,14,12,10,8)

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₃×D₂₉, #10621943, #10621944, …
maximal normal subgroup of	Dic₃×D₂₉, #10621943, #10621944, …
maximal quotient of	C₃×Dic₅₈, C₃×C₄×D₂₉, C₃×D₁₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(348, 9);

C2×C3×D29 #66830

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₃×D₂₉ #66830