C₁₇×Dic₂₉ #14520302

order	1972
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₇×Dic₂₉

Splittings

derived, Sylow	C₂₉ ⋊ C₄×C₁₇
Hall	C₁₇×C₂₉ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₇	D₂₉
commutator, hypocenter	C₂₉	C₄×C₁₇
Frattini	C₂	C₁₇×D₂₉
Fitting, socle, prime radical	C₂×C₁₇×C₂₉	C₂
cosocle	C₂×C₂₉	C₂×C₁₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₁₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 1972

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₁₇×Dic₂₉, C₁₇×Dic₂₀₃, C₁₇×Dic₂₉⋊C₇, …
maximal normal subgroup of	C₇×C₁₇×Dic₂₉, C₁₇×Dic₂₉⋊C₇, C₁₁×C₁₇×Dic₂₉, …
maximal quotient of	C₇×C₁₇×Dic₂₉, C₁₇×Dic₂₀₃, C₁₇×#11760330, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1972, 2);

C17×Dic29 #14520302