D₇₄₇₃ #28418014

order	14946
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₇₄₇₃
unambiguous semidirect product	C₃⋊D₂₄₉₁
unambiguous semidirect product	C₄₇⋊D₁₅₉
unambiguous semidirect product	C₅₃⋊D₁₄₁

Splittings

Fitting, socle, derived, Hall	C₃×C₄₇×C₅₃ ⋊ C₂
Hall	C₄₇×C₅₃ ⋊ D₃
Hall	C₃×C₅₃ ⋊ D₄₇
Hall	C₃×C₄₇ ⋊ D₅₃
Sylow	C₅₃ ⋊ D₁₄₁
Sylow	C₄₇ ⋊ D₁₅₉
Sylow	C₃ ⋊ D₂₄₉₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₄₇×C₅₃	C₂
LCS	G ▷ C₃×C₄₇×C₅₃
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 103
transitive degree	μ_t(G) = 7473

A minimal faithful permutation representation — 2 generators on 103 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)(51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(2,3)(5,50)(6,49)(7,48)(8,47)(9,46)(10,45)(11,44)(12,43)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)(52,103)(53,102)(54,101)(55,100)(56,99)(57,98)(58,97)(59,96)(60,95)(61,94)(62,93)(63,92)(64,91)(65,90)(66,89)(67,88)(68,87)(69,86)(70,85)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)

Polycyclic presentation:

2,3,47,53|b^a=b^2,c^a=c^46,d^a=d^52

Conjugacy classes & character table

3738 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅₃×D₁₄₁, D₄₇×D₁₅₉, D₃×D₂₄₉₁, …
maximal normal subgroup of	D₅₃×D₁₄₁, D₄₇×D₁₅₉, D₃×D₂₄₉₁, …
maximal quotient of	Dic₇₄₇₃, C₂×D₇₄₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14946, 8);

D7473 #28418014