C₃₁×D₃₅ #14524245

order	2170
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×D₃₅
unambiguous semidirect product	C₅⋊(D₇×C₃₁)
unambiguous semidirect product	C₇⋊(D₅×C₃₁)

Splittings

Fitting, socle, Hall	C₅×C₇×C₃₁ ⋊ C₂
derived, Hall	C₅×C₇ ⋊ C₂×C₃₁
Hall	C₇×C₃₁ ⋊ D₅
Hall	C₅×C₃₁ ⋊ D₇
Sylow	C₇ ⋊ D₅×C₃₁
Sylow	C₅ ⋊ D₇×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃₁	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₃₁
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₃₁	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₃₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1085

A minimal faithful permutation representation — 2 generators on 43 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);(33,36)(34,35)(38,43)(39,42)(40,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃₁×D₃₅, D₅×D₇×C₃₁, D₃₅⋊D₃₁, …
maximal normal subgroup of	D₃₁×D₃₅, D₅×D₇×C₃₁, D₃₅⋊D₃₁, …
maximal quotient of	C₃₁×Dic₃₅, C₂×C₃₁×D₃₅, C₃₁×D₁₇₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2170, 8);

C31×D35 #14524245