C₂₉×Dic₁₇ #14520301

order	1972
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂₉×Dic₁₇

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₉	D₁₇
commutator, hypocenter	C₁₇	C₄×C₂₉
Frattini	C₂	C₂₉×D₁₇
Fitting, socle, prime radical	C₂×C₁₇×C₂₉	C₂
cosocle	C₂×C₁₇	C₂×C₂₉
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₂₉

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);(30,32,31,33)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₂₉×Dic₁₇, C₂₉×Dic₁₁₉, Dic₁₇×C₂₉⋊C₇, …
maximal normal subgroup of	C₇×C₂₉×Dic₁₇, Dic₁₇×C₂₉⋊C₇, C₁₁×C₂₉×Dic₁₇, …
maximal quotient of	C₇×C₂₉×Dic₁₇, C₂₉×Dic₁₁₉, C₂₉×#10597480, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1972, 1);

C29×Dic17 #14520301