C₃₁×D₄₁ #14579290

order	2542
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×D₄₁
unambiguous semidirect product	C₄₁⋊(C₂×C₃₁)

Splittings

Fitting, socle, Hall	C₃₁×C₄₁ ⋊ C₂
derived, Sylow	C₄₁ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃₁	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂×C₃₁
Frattini	C₁	G
Fitting, socle	C₃₁×C₄₁	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₃₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 72
transitive degree	μ_t(G) = 1271

A minimal faithful permutation representation — 2 generators on 72 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);(33,72)(34,71)(35,70)(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×C₃₁×D₄₁, C₃₁×D₂₀₅, C₃₁×D₄₁⋊C₅, …
maximal normal subgroup of	C₅×C₃₁×D₄₁, C₃₁×D₄₁⋊C₅, D₄₁×ΓL(1,𝔽₃₂), …
maximal quotient of	C₅×C₃₁×D₄₁, C₃₁×D₂₀₅, C₇×C₃₁×D₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2542, 2);

C31×D41 #14579290