D₅₇₃₅ #26039744

order	11470
automorphism	Aut(G) order 24775200
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₅₇₃₅
unambiguous semidirect product	C₅⋊D₁₁₄₇
unambiguous semidirect product	C₃₁⋊D₁₈₅
unambiguous semidirect product	C₃₇⋊D₁₅₅

Splittings

Fitting, socle, derived, Hall	C₅×C₃₁×C₃₇ ⋊ C₂
Hall	C₃₁×C₃₇ ⋊ D₅
Hall	C₅×C₃₇ ⋊ D₃₁
Hall	C₅×C₃₁ ⋊ D₃₇
Sylow	C₃₇ ⋊ D₁₅₅
Sylow	C₃₁ ⋊ D₁₈₅
Sylow	C₅ ⋊ D₁₁₄₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₃₁×C₃₇	C₂
LCS	G ▷ C₅×C₃₁×C₃₇
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 5735

A minimal faithful permutation representation — 2 generators on 73 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);(2,5)(3,4)(7,36)(8,35)(9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(38,73)(39,72)(40,71)(41,70)(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)(54,57)(55,56)

Polycyclic presentation:

2,5,31,37|b^a=b^4,c^a=c^30,d^a=d^36

Conjugacy classes & character table

2869 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃₇×D₁₅₅, D₃₁×D₁₈₅, D₅×D₁₁₄₇, …
maximal normal subgroup of	D₃₇×D₁₅₅, D₃₁×D₁₈₅, D₅×D₁₁₄₇, …
maximal quotient of	Dic₅₇₃₅, C₂×D₅₇₃₅, C₃×D₅₇₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11470, 9);

D5735 #26039744