D₁₁₈₉₅ #37558180

order	23790
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₈₉₅
unambiguous semidirect product	C₃⋊D₃₉₆₅
unambiguous semidirect product	C₅⋊D₂₃₇₉
unambiguous semidirect product	C₁₃⋊D₉₁₅
unambiguous semidirect product	C₆₁⋊D₁₉₅

Splittings

Fitting, socle, derived, Hall	C₃×C₅×C₁₃×C₆₁ ⋊ C₂
Hall	C₅×C₁₃×C₆₁ ⋊ D₃
Hall	C₃×C₁₃×C₆₁ ⋊ D₅
Hall	C₃×C₅×C₆₁ ⋊ D₁₃
Hall	C₁₃×C₆₁ ⋊ D₁₅
Hall	C₅×C₆₁ ⋊ D₃₉
Hall	C₃×C₅×C₁₃ ⋊ D₆₁
Hall	C₃×C₆₁ ⋊ D₆₅
Hall	C₅×C₁₃ ⋊ D₁₈₃
Sylow	C₆₁ ⋊ D₁₉₅
Hall	C₃×C₁₃ ⋊ D₃₀₅
Hall	C₃×C₅ ⋊ D₇₉₃
Sylow	C₁₃ ⋊ D₉₁₅
Sylow	C₅ ⋊ D₂₃₇₉
Sylow	C₃ ⋊ D₃₉₆₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₃×C₆₁	C₂
LCS	G ▷ C₃×C₅×C₁₃×C₆₁
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 82
transitive degree	μ_t(G) = 11895

A minimal faithful permutation representation — 2 generators on 82 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);(2,3)(5,8)(6,7)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(23,82)(24,81)(25,80)(26,79)(27,78)(28,77)(29,76)(30,75)(31,74)(32,73)(33,72)(34,71)(35,70)(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)

Polycyclic presentation:

2,3,5,13,61|b^a=b^2,c^a=c^4,d^a=d^12,e^a=e^60

Conjugacy classes & character table

5949 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 25);

D11895 #37558180