C₂₉×Dic₁₁₅ #27211102

order	13340
isoclinism	isoclinic class of D₁₁₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×Dic₁₁₅
unambiguous semidirect product	C₂₃⋊(Dic₅×C₂₉)

Splittings

derived, Hall	C₅×C₂₃ ⋊ C₄×C₂₉
Hall	C₅×C₂₃×C₂₉ ⋊ C₄
Hall	C₂₃×C₂₉ ⋊ Dic₅
Hall	C₅×C₂₉ ⋊ Dic₂₃
Sylow	C₂₃ ⋊ Dic₅×C₂₉
Sylow	C₅ ⋊ C₂₉×Dic₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₉	D₁₁₅
commutator, hypocenter	C₅×C₂₃	C₄×C₂₉
Frattini	C₂	C₂₉×D₁₁₅
Fitting, socle, prime radical	C₂×C₅×C₂₃×C₂₉	C₂
cosocle	C₂×C₅×C₂₃	C₂×C₂₉
LCS	G ▷ C₅×C₂₃
UCS	C₁ ◁ C₂×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)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(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);(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(24,25,27,28,26)

Conjugacy classes & character table

3422 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13340, 7);

C29×Dic115 #27211102