C₃⋊D₃×C₂₅×C₂₉ #27189385

order	13050
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅×C₂₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃⋊D₃×C₂₅×C₂₉
unambiguous semidirect product	C₃⋊(D₃×C₂₅×C₂₉)

Splittings

Fitting, Hall	C₃²×C₂₅×C₂₉ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₂₅×C₂₉
Hall	C₃²×C₂₉ ⋊ C₂×C₂₅
Hall	C₃²×C₂₅ ⋊ C₂×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅×C₂₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₂₅×C₂₉
Frattini	C₅	C₅×C₃⋊D₃×C₂₉
Fitting	C₃²×C₂₅×C₂₉	C₂
socle	C₃²×C₅×C₂₉	C₂×C₅
prime radical	C₅×C₃⋊D₃×C₂₉	C₅
cosocle	C₃²×C₅	C₂×C₅×C₂₉
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂₅×C₂₉

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 6525

A minimal faithful permutation representation — 3 generators on 60 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)(30,31,33,36,40,32,34,37,41,45,35,38,42,46,49,39,43,47,50,52,44,48,51,53,54)(56,57)(59,60);(58,59,60);(55,56,57)

Conjugacy classes & character table

4350 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃⋊D₃×C₂₅×D₂₉, C₃⋊D₃×C₂₉×D₂₅, C₃⋊D₃×D₇₂₅, …
maximal normal subgroup of	C₃⋊D₃×C₂₅×D₂₉, C₃⋊D₃×C₂₉×D₂₅, C₃⋊D₃×D₇₂₅, …
maximal quotient of	C₂₅×C₂₉×C₃⋊Dic₃, C₂×C₃⋊D₃×C₂₅×C₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13050, 17);

C3⋊D3×C25×C29 #27189385