D₁₄₇₆₃ #44443296

order	29526
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₄₇₆₃
unambiguous semidirect product	C₃⋊D₄₉₂₁
unambiguous semidirect product	C₇⋊D₂₁₀₉
unambiguous semidirect product	C₁₉⋊D₇₇₇
unambiguous semidirect product	C₃₇⋊D₃₉₉

Splittings

Fitting, socle, derived, Hall	C₃×C₇×C₁₉×C₃₇ ⋊ C₂
Hall	C₇×C₁₉×C₃₇ ⋊ D₃
Hall	C₃×C₁₉×C₃₇ ⋊ D₇
Hall	C₃×C₇×C₃₇ ⋊ D₁₉
Hall	C₁₉×C₃₇ ⋊ D₂₁
Hall	C₃×C₇×C₁₉ ⋊ D₃₇
Hall	C₇×C₃₇ ⋊ D₅₇
Hall	C₇×C₁₉ ⋊ D₁₁₁
Hall	C₃×C₃₇ ⋊ D₁₃₃
Hall	C₃×C₁₉ ⋊ D₂₅₉
Sylow	C₃₇ ⋊ D₃₉₉
Hall	C₃×C₇ ⋊ D₇₀₃
Sylow	C₁₉ ⋊ D₇₇₇
Sylow	C₇ ⋊ D₂₁₀₉
Sylow	C₃ ⋊ D₄₉₂₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₉×C₃₇	C₂
LCS	G ▷ C₃×C₇×C₁₉×C₃₇
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 14763

A minimal faithful permutation representation — 2 generators on 66 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)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(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)(31,66)(32,65)(33,64)(34,63)(35,62)(36,61)(37,60)(38,59)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)

Polycyclic presentation:

2,3,7,19,37|b^a=b^2,c^a=c^6,d^a=d^18,e^a=e^36

Conjugacy classes & character table

7383 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₄₇₆₃
maximal normal subgroup of	C₂×D₁₄₇₆₃
maximal quotient of	Dic₁₄₇₆₃, C₂×D₁₄₇₆₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29526, 29);

D14763 #44443296