C₃₁×D₂₉ #14267802

order	1798
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×D₂₉
unambiguous semidirect product	C₂₉⋊(C₂×C₃₁)

Splittings

Fitting, socle, Hall	C₂₉×C₃₁ ⋊ C₂
derived, Sylow	C₂₉ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃₁	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂×C₃₁
Frattini	C₁	G
Fitting, socle	C₂₉×C₃₁	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₃₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 899

A minimal faithful permutation representation — 2 generators on 60 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);(33,60)(34,59)(35,58)(36,57)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51)(43,50)(44,49)(45,48)(46,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#1181, C₃₁⋊#1181, D₂₉×D₃₁, …
maximal normal subgroup of	C₃₁×#1181, C₃₁⋊#1181, D₂₉×D₃₁, …
maximal quotient of	C₃₁×Dic₂₉, C₂×C₃₁×D₂₉, C₇×C₃₁×D₂₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1798, 1);

C31×D29 #14267802