C₃₁×Dic₁₇ #14523709

order	2108
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₁×Dic₁₇

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃₁	D₁₇
commutator, hypocenter	C₁₇	C₄×C₃₁
Frattini	C₂	C₃₁×D₁₇
Fitting, socle, prime radical	C₂×C₁₇×C₃₁	C₂
cosocle	C₂×C₁₇	C₂×C₃₁
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₃₁

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);(32,34,33,35)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₃₁×Dic₁₇, C₃₁×Dic₁₁₉, C₃₁×#10597480, …
maximal normal subgroup of	C₇×C₃₁×Dic₁₇, C₁₁×C₃₁×Dic₁₇, C₁₃×C₃₁×Dic₁₇, …
maximal quotient of	C₇×C₃₁×Dic₁₇, C₃₁×Dic₁₁₉, C₃₁×#10597480, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2108, 2);

C31×Dic17 #14523709