D₅₉₄₅ #26045285

order	11890
automorphism	Aut(G) order 26633600
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₅₉₄₅
unambiguous semidirect product	C₅⋊D₁₁₈₉
unambiguous semidirect product	C₂₉⋊D₂₀₅
unambiguous semidirect product	C₄₁⋊D₁₄₅

Splittings

Fitting, socle, derived, Hall	C₅×C₂₉×C₄₁ ⋊ C₂
Hall	C₂₉×C₄₁ ⋊ D₅
Hall	C₅×C₄₁ ⋊ D₂₉
Hall	C₅×C₂₉ ⋊ D₄₁
Sylow	C₄₁ ⋊ D₁₄₅
Sylow	C₂₉ ⋊ D₂₀₅
Sylow	C₅ ⋊ D₁₁₈₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₂₉×C₄₁	C₂
LCS	G ▷ C₅×C₂₉×C₄₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 5945

A minimal faithful permutation representation — 2 generators on 75 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);(2,5)(3,4)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(36,75)(37,74)(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:

2,5,29,41|b^a=b^4,c^a=c^28,d^a=d^40

Conjugacy classes & character table

2974 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#37558084, #37558085, #37558088, …
maximal normal subgroup of	#37558084, #37558085, #37558088, …
maximal quotient of	Dic₅₉₄₅, C₂×D₅₉₄₅, C₃×D₅₉₄₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11890, 9);

D5945 #26045285