D₃₁×C₇₃ #17985347

order	4526
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃₁×C₇₃
unambiguous semidirect product	C₃₁⋊(C₂×C₇₃)

Splittings

Fitting, socle, Hall	C₃₁×C₇₃ ⋊ C₂
derived, Sylow	C₃₁ ⋊ C₂×C₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₇₃	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₇₃
Frattini	C₁	G
Fitting, socle	C₃₁×C₇₃	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₇₃

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 104
transitive degree	μ_t(G) = 2263

A minimal faithful permutation representation — 2 generators on 104 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)(32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104);(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)

Conjugacy classes & character table

1241 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₃₁×C₇₃, C₇₃×D₉₃, D₃₁×C₇₃⋊C₃, …
maximal normal subgroup of	C₃×D₃₁×C₇₃, D₃₁×C₇₃⋊C₃, C₇₃×D₃₁⋊C₃, …
maximal quotient of	C₃×D₃₁×C₇₃, C₇₃×D₉₃, C₅×D₃₁×C₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4526, 1);

D31×C73 #17985347