C₁₇×Dic₃₁ #14523710

order	2108
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×Dic₃₁
unambiguous semidirect product	C₃₁⋊(C₄×C₁₇)

Splittings

derived, Sylow	C₃₁ ⋊ C₄×C₁₇
Hall	C₁₇×C₃₁ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₇	D₃₁
commutator, hypocenter	C₃₁	C₄×C₁₇
Frattini	C₂	C₁₇×D₃₁
Fitting, socle, prime radical	C₂×C₁₇×C₃₁	C₂
cosocle	C₂×C₃₁	C₂×C₁₇
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₁₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 2108

A minimal faithful permutation representation — 2 generators on 52 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);(18,20,19,21)(23,52)(24,51)(25,50)(26,49)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₁₇×Dic₃₁, C₁₇×Dic₂₁₇, C₁₇×C₃₁⋊#157, …
maximal normal subgroup of	C₇×C₁₇×Dic₃₁, C₁₁×C₁₇×Dic₃₁, C₁₃×C₁₇×Dic₃₁, …
maximal quotient of	C₇×C₁₇×Dic₃₁, C₁₇×Dic₂₁₇, C₁₇×C₃₁⋊#157, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2108, 3);

C17×Dic31 #14523710