C₅×C₉×D₄₉ #17984285

order	4410
isoclinism	isoclinic class of D₄₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×C₉×D₄₉

Splittings

Fitting, Hall	C₅×C₉×C₄₉ ⋊ C₂
derived, Sylow	C₄₉ ⋊ C₂×C₅×C₉
Hall	C₉×C₄₉ ⋊ C₂×C₅
Hall	C₅×C₄₉ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	D₄₉
commutator, hypocenter	C₄₉	C₂×C₅×C₉
Frattini	C₃×C₇	C₃×C₅×D₇
Fitting	C₅×C₉×C₄₉	C₂
socle	C₃×C₅×C₇	C₃×D₇
prime radical	C₃×C₅×D₄₉	C₃
cosocle	C₃×C₄₉	C₂×C₃×C₅
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₅×C₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 2205

A minimal faithful permutation representation — 2 generators on 63 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);(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,57)(23,56)(24,55)(25,54)(26,53)(27,52)(28,51)(29,50)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₂₅×D₄₉, C₅²×C₉×D₄₉, C₅×C₉×D₂₄₅
maximal normal subgroup of	C₉×C₂₅×D₄₉, C₅²×C₉×D₄₉
maximal quotient of	C₉×C₂₅×D₄₉, C₅²×C₉×D₄₉, C₅×C₉×D₂₄₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4410, 6);

C5×C9×D49 #17984285