D₁₁₅₇₁ #37529013

order	23142
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₅₇₁
unambiguous semidirect product	C₃⋊D₃₈₅₇
unambiguous semidirect product	C₇⋊D₁₆₅₃
unambiguous semidirect product	C₁₉⋊D₆₀₉
unambiguous semidirect product	C₂₉⋊D₃₉₉

Splittings

Fitting, socle, derived, Hall	C₃×C₇×C₁₉×C₂₉ ⋊ C₂
Hall	C₇×C₁₉×C₂₉ ⋊ D₃
Hall	C₃×C₁₉×C₂₉ ⋊ D₇
Hall	C₃×C₇×C₂₉ ⋊ D₁₉
Hall	C₁₉×C₂₉ ⋊ D₂₁
Hall	C₃×C₇×C₁₉ ⋊ D₂₉
Hall	C₇×C₂₉ ⋊ D₅₇
Hall	C₇×C₁₉ ⋊ D₈₇
Hall	C₃×C₂₉ ⋊ D₁₃₃
Hall	C₃×C₁₉ ⋊ D₂₀₃
Sylow	C₂₉ ⋊ D₃₉₉
Hall	C₃×C₇ ⋊ D₅₅₁
Sylow	C₁₉ ⋊ D₆₀₉
Sylow	C₇ ⋊ D₁₆₅₃
Sylow	C₃ ⋊ D₃₈₅₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₉×C₂₉	C₂
LCS	G ▷ C₃×C₇×C₁₉×C₂₉
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 11571

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);(2,3)(5,10)(6,9)(7,8)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(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:

2,3,7,19,29|b^a=b^2,c^a=c^6,d^a=d^18,e^a=e^28

Conjugacy classes & character table

5787 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23142, 22);

D11571 #37529013