C₅²×C₉×D₂₉ #27189396

order	13050
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₅²×C₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×C₉×D₂₉
unambiguous semidirect product	C₂₉⋊(C₂×C₅²×C₉)

Splittings

Fitting, Hall	C₅²×C₉×C₂₉ ⋊ C₂
derived, Sylow	C₂₉ ⋊ C₂×C₅²×C₉
Hall	C₅²×C₂₉ ⋊ C₂×C₉
Hall	C₉×C₂₉ ⋊ C₂×C₅²

Subgroups

	subgroup	G/H
center, hypercenter	C₅²×C₉	D₂₉
commutator, hypocenter	C₂₉	C₂×C₅²×C₉
Frattini	C₃	C₃×C₅²×D₂₉
Fitting	C₅²×C₉×C₂₉	C₂
socle	C₃×C₅²×C₂₉	C₂×C₃
prime radical	C₃×C₅²×D₂₉	C₃
cosocle	C₃×C₂₉	C₂×C₃×C₅²
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₅²×C₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 6525

A minimal faithful permutation representation — 2 generators on 48 points:

(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)(30,31,33,32,34,36,35,37,38)(44,45,46,47,48);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(39,40,41,42,43)

Conjugacy classes & character table

3600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅²×C₉×#1181, C₅×C₉×#10596817, C₅×C₉×D₅×D₂₉, …
maximal normal subgroup of	C₅²×C₉×#1181, C₅×C₉×#10596817, C₅×C₉×D₅×D₂₉, …
maximal quotient of	C₅²×C₉×Dic₂₉, C₂×C₅²×C₉×D₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13050, 28);

C52×C9×D29 #27189396