C₂₉×C₅²⋊C₃ #14524274

order	2175
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₂₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₂₉×C₅²⋊C₃
unambiguous semidirect product	C₅²⋊(C₃×C₂₉)
unambiguous semidirect product	(C₅²×C₂₉)⋊C₃

Splittings

Fitting, socle, Hall	C₅²×C₂₉ ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₅²×C₂₉	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 435

A minimal faithful permutation representation — 2 generators on 44 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)(30,31,33)(32,36,38)(34,39,42)(35,41,44)(37,40,43);(30,32,37,42,44)(31,36,40,34,35)(33,39,38,41,43)

Conjugacy classes & character table

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

Relationships

derived subgroup of	C₂₉⋊#3874, C₃×#22576397, C₃×#22576417, …
maximal subgroup of	C₂₉×#3874, C₂₉⋊#3874, C₂₉×(C₅⋊D₅)⋊C₃, …
maximal normal subgroup of	C₂₉×#3874, C₂₉⋊#3874, C₂₉×(C₅⋊D₅)⋊C₃, …
maximal quotient of	C₂×C₂₉×C₅²⋊C₃, C₂₉×C₇⋊(C₅²⋊C₃), C₇×C₂₉×C₅²⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2175, 3);

C29×C52⋊C3 #14524274