D₁₀₃₅₃ #35208486

order	20706
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₀₃₅₃
unambiguous semidirect product	C₃⋊D₃₄₅₁
unambiguous semidirect product	C₇⋊D₁₄₇₉
unambiguous semidirect product	C₁₇⋊D₆₀₉
unambiguous semidirect product	C₂₉⋊D₃₅₇

Splittings

Fitting, socle, derived, Hall	C₃×C₇×C₁₇×C₂₉ ⋊ C₂
Hall	C₇×C₁₇×C₂₉ ⋊ D₃
Hall	C₃×C₁₇×C₂₉ ⋊ D₇
Hall	C₃×C₇×C₂₉ ⋊ D₁₇
Hall	C₁₇×C₂₉ ⋊ D₂₁
Hall	C₃×C₇×C₁₇ ⋊ D₂₉
Hall	C₇×C₂₉ ⋊ D₅₁
Hall	C₇×C₁₇ ⋊ D₈₇
Hall	C₃×C₂₉ ⋊ D₁₁₉
Hall	C₃×C₁₇ ⋊ D₂₀₃
Sylow	C₂₉ ⋊ D₃₅₇
Hall	C₃×C₇ ⋊ D₄₉₃
Sylow	C₁₇ ⋊ D₆₀₉
Sylow	C₇ ⋊ D₁₄₇₉
Sylow	C₃ ⋊ D₃₄₅₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₇×C₂₉	C₂
LCS	G ▷ C₃×C₇×C₁₇×C₂₉
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 56
transitive degree	μ_t(G) = 10353

A minimal faithful permutation representation — 2 generators on 56 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);(2,3)(5,10)(6,9)(7,8)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)

Polycyclic presentation:

2,3,7,17,29|b^a=b^2,c^a=c^6,d^a=d^16,e^a=e^28

Conjugacy classes & character table

5178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃₁₀₅₉
maximal quotient of	D₃₁₀₅₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20706, 18);

D10353 #35208486