C₂₉×Dic₁₉ #14555604

order	2204
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×Dic₁₉
unambiguous semidirect product	C₁₉⋊(C₄×C₂₉)

Splittings

derived, Sylow	C₁₉ ⋊ C₄×C₂₉
Hall	C₁₉×C₂₉ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₉	D₁₉
commutator, hypocenter	C₁₉	C₄×C₂₉
Frattini	C₂	C₂₉×D₁₉
Fitting, socle, prime radical	C₂×C₁₉×C₂₉	C₂
cosocle	C₂×C₁₉	C₂×C₂₉
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₂₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 2204

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);(30,32,31,33)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×C₂₉×Dic₁₉, C₂₉×Dic₉₅, C₂₉×C₁₉⋊AGL(1,𝔽₅), …
maximal normal subgroup of	C₅×C₂₉×Dic₁₉, C₇×C₂₉×Dic₁₉, Dic₁₉×C₂₉⋊C₇, …
maximal quotient of	C₅×C₂₉×Dic₁₉, C₂₉×Dic₉₅, C₂₉×C₁₉⋊AGL(1,𝔽₅), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2204, 2);

C29×Dic19 #14555604