C₁₃×Dic₂₅ #13049899

order	1300
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₃×Dic₂₅

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₂₅
commutator, hypocenter	C₂₅	C₄×C₁₃
Frattini	C₂×C₅	D₅×C₁₃
Fitting	C₂×C₁₃×C₂₅	C₂
socle, prime radical	C₂×C₅×C₁₃	D₅
cosocle	C₂×C₂₅	C₂×C₁₃
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₁₃

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);(14,16,15,17)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₃⋊C₃×Dic₂₅, C₃×C₁₃×Dic₂₅, C₁₃×Dic₇₅, …
maximal normal subgroup of	C₁₃⋊C₃×Dic₂₅, C₃×C₁₃×Dic₂₅, C₁₁×C₁₃×Dic₂₅, …
maximal quotient of	C₃×C₁₃×Dic₂₅, C₁₃×Dic₇₅, C₁₃×#11744620, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1300, 1);

C13×Dic25 #13049899