C₅×D₃₇×D₄₉ #49136366

order	36260
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₃₇×D₄₉
unambiguous semidirect product	(C₃₇×D₄₉)⋊(C₂×C₅)
unambiguous semidirect product	(C₄₉×D₃₇)⋊(C₂×C₅)
unambiguous semidirect product	D₁₈₁₃⋊(C₂×C₅)

Splittings

Fitting, Hall	C₅×C₃₇×C₄₉ ⋊ C₂²
derived, Hall	C₃₇×C₄₉ ⋊ C₂²×C₅
Hall	C₅×C₄₉ ⋊ C₂×D₃₇
Hall	C₅×C₃₇ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×C₅×D₃₇
Sylow	C₃₇ ⋊ C₂×C₅×D₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅	D₃₇×D₄₉
commutator, cosocle, hypocenter	C₃₇×C₄₉	C₂²×C₅
Frattini	C₇	C₅×D₇×D₃₇
Fitting	C₅×C₃₇×C₄₉	C₂²
socle	C₅×C₇×C₃₇	C₂×D₇
LCS	G ▷ C₃₇×C₄₉
UCS	C₁ ◁ C₅

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 9065

A minimal faithful permutation representation — 2 generators on 91 points:

(1,2,3,4,5)(6,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8)(44,46)(45,49)(47,52)(48,55)(50,58)(51,57)(53,62)(54,65)(56,67)(59,71)(60,70)(61,69)(63,74)(64,76)(66,78)(68,80)(72,81)(73,82)(75,84)(77,86)(79,88)(83,89)(85,90)(87,91);(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)(43,48,66,87,86,65,46,45,56,79,90,76,52,51,50,68,89,84,62,61,60,59,81,82,74,63,73,72,71,70,69,53,75,83,80,58,57,47,64,85,88,67,49,44,54,77,91,78,55)

Conjugacy classes & character table

2600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36260, 12);

C5×D37×D49 #49136366