D₁₇₂₅₅ #46828516

order	34510
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₇₂₅₅
unambiguous semidirect product	C₅⋊D₃₄₅₁
unambiguous semidirect product	C₇⋊D₂₄₆₅
unambiguous semidirect product	C₁₇⋊D₁₀₁₅
unambiguous semidirect product	C₂₉⋊D₅₉₅

Splittings

Fitting, socle, derived, Hall	C₅×C₇×C₁₇×C₂₉ ⋊ C₂
Hall	C₇×C₁₇×C₂₉ ⋊ D₅
Hall	C₅×C₁₇×C₂₉ ⋊ D₇
Hall	C₅×C₇×C₂₉ ⋊ D₁₇
Hall	C₅×C₇×C₁₇ ⋊ D₂₉
Hall	C₁₇×C₂₉ ⋊ D₃₅
Hall	C₇×C₂₉ ⋊ D₈₅
Hall	C₅×C₂₉ ⋊ D₁₁₉
Hall	C₇×C₁₇ ⋊ D₁₄₅
Hall	C₅×C₁₇ ⋊ D₂₀₃
Hall	C₅×C₇ ⋊ D₄₉₃
Sylow	C₂₉ ⋊ D₅₉₅
Sylow	C₁₇ ⋊ D₁₀₁₅
Sylow	C₇ ⋊ D₂₄₆₅
Sylow	C₅ ⋊ D₃₄₅₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₁₇×C₂₉	C₂
LCS	G ▷ C₅×C₇×C₁₇×C₂₉
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 17255

A minimal faithful permutation representation — 2 generators on 58 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);(2,5)(3,4)(7,12)(8,11)(9,10)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(31,58)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)

Polycyclic presentation:

2,5,7,17,29|b^a=b^4,c^a=c^6,d^a=d^16,e^a=e^28

Conjugacy classes & character table

8629 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34510, 17);

D17255 #46828516