D₁₈₂₇₅ #49143129

order	36550
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₈₂₇₅
unambiguous semidirect product	C₁₇⋊D₁₀₇₅
unambiguous semidirect product	C₂₅⋊D₇₃₁
unambiguous semidirect product	C₄₃⋊D₄₂₅

Splittings

Fitting, derived, Hall	C₁₇×C₂₅×C₄₃ ⋊ C₂
Hall	C₂₅×C₄₃ ⋊ D₁₇
Hall	C₁₇×C₄₃ ⋊ D₂₅
Hall	C₁₇×C₂₅ ⋊ D₄₃
Sylow	C₄₃ ⋊ D₄₂₅
Sylow	C₂₅ ⋊ D₇₃₁
Sylow	C₁₇ ⋊ D₁₀₇₅

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₇×C₂₅×C₄₃	C₂
Frattini	C₅	D₃₆₅₅
socle	C₅×C₁₇×C₄₃	D₅
LCS	G ▷ C₁₇×C₂₅×C₄₃
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 85
transitive degree	μ_t(G) = 18275

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

Polycyclic presentation:

2,5,17,43,5|b^5=e^4,b^a=b^4e,c^a=c^16,d^a=d^42,e^a=e^4

Conjugacy classes & character table

9139 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36550, 8);

D18275 #49143129