D₇₉₅₅ #30629856

order	15910
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₇₉₅₅
unambiguous semidirect product	C₅⋊D₁₅₉₁
unambiguous semidirect product	C₃₇⋊D₂₁₅
unambiguous semidirect product	C₄₃⋊D₁₈₅

Splittings

Fitting, socle, derived, Hall	C₅×C₃₇×C₄₃ ⋊ C₂
Hall	C₃₇×C₄₃ ⋊ D₅
Hall	C₅×C₄₃ ⋊ D₃₇
Hall	C₅×C₃₇ ⋊ D₄₃
Sylow	C₄₃ ⋊ D₁₈₅
Sylow	C₃₇ ⋊ D₂₁₅
Sylow	C₅ ⋊ D₁₅₉₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₃₇×C₄₃	C₂
LCS	G ▷ C₅×C₃₇×C₄₃
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 85
transitive degree	μ_t(G) = 7955

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);(2,5)(3,4)(7,42)(8,41)(9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(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:

2,5,37,43|b^a=b^4,c^a=c^36,d^a=d^42

Conjugacy classes & character table

3979 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₄₃×D₁₈₅, D₃₇×D₂₁₅, D₅×D₁₅₉₁, …
maximal normal subgroup of	D₄₃×D₁₈₅, D₃₇×D₂₁₅, D₅×D₁₅₉₁, …
maximal quotient of	Dic₇₉₅₅, C₂×D₇₉₅₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15910, 8);

D7955 #30629856