C₅×Dic₉₈ #14519917

order	1960
isoclinism	isoclinic class of Dic₉₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×Dic₉₈
unambiguous semidirect product	C₄₉⋊(C₅×Q₈)

Splittings

Hall	C₅×C₄₉ ⋊ Q₈
Sylow	C₄₉ ⋊ C₅×Q₈

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, prime radical	C₂×C₅×C₇	C₂×D₇
hypercenter	C₄×C₅	D₄₉
hypocenter	C₄₉	C₅×Q₈
LCS	G ▷ C₂×C₄₉ ▷ C₄₉
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 1960

A minimal faithful permutation representation — 2 generators on 62 points:

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

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, 14);

C5×Dic98 #14519917