D₁₄₅₃₅ #44414643

order	29070
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₄₅₃₅
unambiguous semidirect product	C₅⋊D₂₉₀₇
unambiguous semidirect product	C₉⋊D₁₆₁₅
unambiguous semidirect product	C₁₇⋊D₈₅₅
unambiguous semidirect product	C₁₉⋊D₇₆₅

Splittings

Fitting, derived, Hall	C₅×C₉×C₁₇×C₁₉ ⋊ C₂
Hall	C₉×C₁₇×C₁₉ ⋊ D₅
Hall	C₅×C₁₇×C₁₉ ⋊ D₉
Hall	C₅×C₉×C₁₉ ⋊ D₁₇
Hall	C₅×C₉×C₁₇ ⋊ D₁₉
Hall	C₁₇×C₁₉ ⋊ D₄₅
Hall	C₉×C₁₉ ⋊ D₈₅
Hall	C₉×C₁₇ ⋊ D₉₅
Hall	C₅×C₁₉ ⋊ D₁₅₃
Hall	C₅×C₁₇ ⋊ D₁₇₁
Hall	C₅×C₉ ⋊ D₃₂₃
Sylow	C₁₉ ⋊ D₇₆₅
Sylow	C₁₇ ⋊ D₈₅₅
Sylow	C₉ ⋊ D₁₆₁₅
Sylow	C₅ ⋊ D₂₉₀₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₇×C₁₉	C₂
Frattini	C₃	D₄₈₄₅
socle	C₃×C₅×C₁₇×C₁₉	D₃
LCS	G ▷ C₅×C₉×C₁₇×C₁₉
UCS	C₁

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 14535

A minimal faithful permutation representation — 2 generators on 50 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);(2,9)(3,8)(4,7)(5,6)(11,14)(12,13)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)

Polycyclic presentation:

2,3,5,17,19,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^16,e^a=e^18,f^a=f^2

Conjugacy classes & character table

7269 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₄₅₃₅
maximal normal subgroup of	C₂×D₁₄₅₃₅
maximal quotient of	Dic₁₄₅₃₅, C₂×D₁₄₅₃₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29070, 17);

D14535 #44414643