C₂×C₅×D₁₄₂₁ #43249273

order	28420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₁₄₂₁
unambiguous semidirect product	(C₂×C₂₉)⋊(C₅×D₄₉)
unambiguous semidirect product	(C₂×C₄₉)⋊(C₅×D₂₉)

Splittings

Fitting	C₂×C₅×C₂₉×C₄₉ ⋊ C₂
derived, Hall	C₂₉×C₄₉ ⋊ C₂²×C₅
Hall	C₅×C₂₉×C₄₉ ⋊ C₂²
Hall	C₅×C₄₉ ⋊ C₂×D₂₉
Hall	C₅×C₂₉ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×C₅×D₂₉
Sylow	C₂₉ ⋊ C₂×C₅×D₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₄₂₁
commutator, cosocle, hypocenter	C₂₉×C₄₉	C₂²×C₅
Frattini	C₇	C₂×C₅×D₂₀₃
Fitting	C₂×C₅×C₂₉×C₄₉	C₂
socle	C₂×C₅×C₇×C₂₉	D₇
LCS	G ▷ C₂₉×C₄₉
UCS	C₁ ◁ C₂×C₅

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 85
transitive degree	μ_t(G) = 14210

A minimal faithful permutation representation — 2 generators on 85 points:

(3,4,5,6,7)(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)(38,40)(39,43)(41,46)(42,49)(44,52)(45,51)(47,56)(48,59)(50,61)(53,65)(54,64)(55,63)(57,58)(60,70)(62,72)(66,73)(67,75)(68,74)(69,78)(71,80)(76,81)(77,82)(79,84)(83,85);(1,2)(8,9,11,13,15,17,19,21,23,25,27,29,31,33,35,36,34,32,30,28,26,24,22,20,18,16,14,12,10)(37,51,75,85,77,55,40,43,64,81,79,68,46,49,52,73,71,69,56,59,61,65,62,60,58,57,70,72,53,50,48,47,78,80,66,44,42,41,74,84,76,54,39,38,63,82,83,67,45)

Conjugacy classes & character table

7120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28420, 48);

C2×C5×D1421 #43249273