C₁₉×Dic₅₃ #16860907

order	4028
isoclinism	isoclinic class of D₅₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×Dic₅₃

Splittings

derived, Sylow	C₅₃ ⋊ C₄×C₁₉
Hall	C₁₉×C₅₃ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₅₃
commutator, hypocenter	C₅₃	C₄×C₁₉
Frattini	C₂	C₁₉×D₅₃
Fitting, socle, prime radical	C₂×C₁₉×C₅₃	C₂
cosocle	C₂×C₅₃	C₂×C₁₉
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂×C₁₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 76
transitive degree	μ_t(G) = 4028

A minimal faithful permutation representation — 2 generators on 76 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76);(20,22,21,23)(25,76)(26,75)(27,74)(28,73)(29,72)(30,71)(31,70)(32,69)(33,68)(34,67)(35,66)(36,65)(37,64)(38,63)(39,62)(40,61)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₉×Dic₅₃, C₁₉×Dic₁₅₉, C₁₉⋊C₃×Dic₅₃, …
maximal normal subgroup of	C₃×C₁₉×Dic₅₃, C₁₉⋊C₃×Dic₅₃, C₅×C₁₉×Dic₅₃, …
maximal quotient of	C₃×C₁₉×Dic₅₃, C₁₉×Dic₁₅₉, C₅×C₁₉×Dic₅₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4028, 3);

C19×Dic53 #16860907