C₃×C₂₅×D₁₃ #14519595

order	1950
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₂₅×D₁₃

Splittings

Fitting, Hall	C₃×C₁₃×C₂₅ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₃×C₂₅
Hall	C₁₃×C₂₅ ⋊ C₂×C₃
Hall	C₃×C₁₃ ⋊ C₂×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₅	D₁₃
commutator, hypocenter	C₁₃	C₂×C₃×C₂₅
Frattini	C₅	C₃×C₅×D₁₃
Fitting	C₃×C₁₃×C₂₅	C₂
socle	C₃×C₅×C₁₃	C₂×C₅
prime radical	C₃×C₅×D₁₃	C₅
cosocle	C₅×C₁₃	C₂×C₃×C₅
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₂₅

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 975

A minimal faithful permutation representation — 2 generators on 41 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)(29,30,31,32,33,34,35,36,37,38,39,40,41);(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₂₅×#261, C₃×#13049904, C₂₅×C₃⋊#261, …
maximal normal subgroup of	C₃×C₂₅×#261, C₃×#13049904, C₂₅×C₃⋊#261, …
maximal quotient of	C₃×C₂₅×Dic₁₃, C₂×C₃×C₂₅×D₁₃, C₃×C₇×C₂₅×D₁₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1950, 5);

C3×C25×D13 #14519595