C₅×D₁₉₆ #14519919

order	1960
isoclinism	isoclinic class of Dic₉₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₁₉₆
unambiguous semidirect product	C₄⋊(C₅×D₄₉)

Splittings

Fitting	C₄×C₅×C₄₉ ⋊ C₂
Hall	C₅×C₄₉ ⋊ D₄
Sylow	C₄₉ ⋊ C₅×D₄

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂×D₄₉
commutator, cosocle	C₂×C₄₉	C₂²×C₅
Frattini	C₂×C₇	C₂×C₅×D₇
Fitting	C₄×C₅×C₄₉	C₂
socle	C₂×C₅×C₇	C₂×D₇
hypercenter	C₄×C₅	D₄₉
hypocenter	C₄₉	C₅×D₄
LCS	G ▷ C₂×C₄₉ ▷ C₄₉
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 980

A minimal faithful permutation representation — 2 generators on 58 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);(7,9)(11,58)(12,57)(13,56)(14,55)(15,54)(16,53)(17,52)(18,51)(19,50)(20,49)(21,48)(22,47)(23,46)(24,45)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 16);

C5×D196 #14519919