C₂₅×Dic₁₃ #13049900

order	1300
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂₅×Dic₁₃

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₂₅
Hall	C₁₃×C₂₅ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₅	D₁₃
commutator, hypocenter	C₁₃	C₄×C₂₅
Frattini	C₂×C₅	C₅×D₁₃
Fitting	C₂×C₁₃×C₂₅	C₂
socle, prime radical, cosocle	C₂×C₅×C₁₃	C₂×C₅
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₂₅

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 1300

A minimal faithful permutation representation — 2 generators on 42 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)(30,31,32,33,34,35,36,37,38,39,40,41,42);(26,28,27,29)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₅×Dic₁₃⋊C₃, C₃×C₂₅×Dic₁₃, C₂₅×Dic₃₉, …
maximal normal subgroup of	C₂₅×Dic₁₃⋊C₃, C₃×C₂₅×Dic₁₃, C₁₁×C₂₅×Dic₁₃, …
maximal quotient of	C₃×C₂₅×Dic₁₃, C₂₅×Dic₃₉, C₂₅×#90865, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1300, 2);

C25×Dic13 #13049900