C₅×Dic₂₅ #92520

order	500
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×Dic₂₅

Splittings

derived	C₂₅ ⋊ C₄×C₅
Sylow	C₅×C₂₅ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	D₂₅
commutator, hypocenter	C₂₅	C₄×C₅
Frattini	C₂×C₅	C₅×D₅
Fitting	C₂×C₅×C₂₅	C₂
socle, prime radical	C₂×C₅²	D₅
cosocle	C₂×C₂₅	C₂×C₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₅

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 100

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3,4)(5,6,7,8,9)(11,13)(12,16)(14,19)(15,22)(17,25)(18,24)(20,21)(23,29)(26,30)(27,31)(28,33)(32,34);(10,24,34,27,13,16,30,28,19,22,25,23,21,20,29,17,15,14,33,26,12,11,31,32,18)

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#6016, #11758644, #11758650, …
maximal normal subgroup of	C₅×#6016, #11758644, #11758650, …
maximal quotient of	C₅×#6014, C₂×C₅×Dic₂₅, C₃×C₅×Dic₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(500, 6);

C5×Dic25 #92520

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₅×Dic₂₅ #92520