D₁₇₃₂₅ #46831376

order	34650
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₇₃₂₅
unambiguous semidirect product	C₇⋊D₂₄₇₅
unambiguous semidirect product	C₉⋊D₁₉₂₅
unambiguous semidirect product	C₁₁⋊D₁₅₇₅
unambiguous semidirect product	C₂₅⋊D₆₉₃

Splittings

Fitting, derived, Hall	C₇×C₉×C₁₁×C₂₅ ⋊ C₂
Hall	C₉×C₁₁×C₂₅ ⋊ D₇
Hall	C₇×C₁₁×C₂₅ ⋊ D₉
Hall	C₇×C₉×C₂₅ ⋊ D₁₁
Hall	C₇×C₉×C₁₁ ⋊ D₂₅
Hall	C₁₁×C₂₅ ⋊ D₆₃
Hall	C₉×C₂₅ ⋊ D₇₇
Hall	C₇×C₂₅ ⋊ D₉₉
Hall	C₉×C₁₁ ⋊ D₁₇₅
Hall	C₇×C₁₁ ⋊ D₂₂₅
Hall	C₇×C₉ ⋊ D₂₇₅
Sylow	C₂₅ ⋊ D₆₉₃
Sylow	C₁₁ ⋊ D₁₅₇₅
Sylow	C₉ ⋊ D₁₉₂₅
Sylow	C₇ ⋊ D₂₄₇₅

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₉×C₁₁×C₂₅	C₂
Frattini	C₃×C₅	D₁₁₅₅
socle	C₃×C₅×C₇×C₁₁	D₁₅
LCS	G ▷ C₇×C₉×C₁₁×C₂₅
UCS	C₁

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 17325

A minimal faithful permutation representation — 2 generators on 52 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);(2,9)(3,8)(4,7)(5,6)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(36,41)(37,40)(38,39)(43,52)(44,51)(45,50)(46,49)(47,48)

Polycyclic presentation:

2,3,5,7,11,3,5|b^3=f^2,c^5=g^4,b^a=b^2f,c^a=c^4g,d^a=d^6,e^a=e^10,f^a=f^2,g^a=g^4

Conjugacy classes & character table

8664 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 19);

D17325 #46831376