C₂₅×D₃₁ #13095458

order	1550
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂₅×D₃₁

Splittings

Fitting, Hall	C₂₅×C₃₁ ⋊ C₂
derived, Sylow	C₃₁ ⋊ C₂×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅	D₃₁
commutator, hypocenter	C₃₁	C₂×C₂₅
Frattini	C₅	C₅×D₃₁
Fitting	C₂₅×C₃₁	C₂
socle, cosocle	C₅×C₃₁	C₂×C₅
prime radical	C₅×D₃₁	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂₅

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 56
transitive degree	μ_t(G) = 775

A minimal faithful permutation representation — 2 generators on 56 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)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56);(27,56)(28,55)(29,54)(30,53)(31,52)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₂₅×D₃₁, C₂×C₂₅×D₃₁, C₂₅×D₃₁⋊C₃, …
maximal normal subgroup of	D₂₅×D₃₁, C₂×C₂₅×D₃₁, C₂₅×D₃₁⋊C₃, …
maximal quotient of	C₂₅×Dic₃₁, C₂×C₂₅×D₃₁, C₃×C₂₅×D₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1550, 4);

C25×D31 #13095458