C₃₁×Dic₃₅ #16864682

order	4340
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×Dic₃₅
unambiguous semidirect product	C₇⋊(Dic₅×C₃₁)

Splittings

derived, Hall	C₅×C₇ ⋊ C₄×C₃₁
Hall	C₅×C₇×C₃₁ ⋊ C₄
Hall	C₇×C₃₁ ⋊ Dic₅
Hall	C₅×C₃₁ ⋊ Dic₇
Sylow	C₇ ⋊ Dic₅×C₃₁
Sylow	C₅ ⋊ Dic₇×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃₁	D₃₅
commutator, hypocenter	C₅×C₇	C₄×C₃₁
Frattini	C₂	C₃₁×D₃₅
Fitting, socle, prime radical	C₂×C₅×C₇×C₃₁	C₂
cosocle	C₂×C₅×C₇	C₂×C₃₁
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₃₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 4340

A minimal faithful permutation representation — 2 generators on 47 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);(32,34,33,35)(37,40)(38,39)(42,47)(43,46)(44,45)

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₃₁×Dic₃₅, C₃₁×Dic₁₀₅, C₃₁⋊C₃×Dic₃₅, …
maximal normal subgroup of	C₃×C₃₁×Dic₃₅, C₃₁⋊C₃×Dic₃₅, C₃₁×ΓL(1,𝔽₈)⋊Dic₅, …
maximal quotient of	C₃×C₃₁×Dic₃₅, C₃₁×Dic₁₀₅, C₃₁×Dic₁₇₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4340, 8);

C31×Dic35 #16864682