D₁₅₆₉₅ #44536023

order	31390
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₆₉₅
unambiguous semidirect product	C₅⋊D₃₁₃₉
unambiguous semidirect product	C₄₃⋊D₃₆₅
unambiguous semidirect product	C₇₃⋊D₂₁₅

Splittings

Fitting, socle, derived, Hall	C₅×C₄₃×C₇₃ ⋊ C₂
Hall	C₄₃×C₇₃ ⋊ D₅
Hall	C₅×C₇₃ ⋊ D₄₃
Hall	C₅×C₄₃ ⋊ D₇₃
Sylow	C₇₃ ⋊ D₂₁₅
Sylow	C₄₃ ⋊ D₃₆₅
Sylow	C₅ ⋊ D₃₁₃₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₄₃×C₇₃	C₂
LCS	G ▷ C₅×C₄₃×C₇₃
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 15695

A minimal faithful permutation representation — 2 generators on 121 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)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121);(2,5)(3,4)(7,48)(8,47)(9,46)(10,45)(11,44)(12,43)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)(50,121)(51,120)(52,119)(53,118)(54,117)(55,116)(56,115)(57,114)(58,113)(59,112)(60,111)(61,110)(62,109)(63,108)(64,107)(65,106)(66,105)(67,104)(68,103)(69,102)(70,101)(71,100)(72,99)(73,98)(74,97)(75,96)(76,95)(77,94)(78,93)(79,92)(80,91)(81,90)(82,89)(83,88)(84,87)(85,86)

Polycyclic presentation:

2,5,43,73|b^a=b^4,c^a=c^42,d^a=d^72

Conjugacy classes & character table

7849 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₅₆₉₅
maximal normal subgroup of	C₂×D₁₅₆₉₅
maximal quotient of	Dic₁₅₆₉₅, C₂×D₁₅₆₉₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31390, 8);

D15695 #44536023