D₁₆₀₉₅ #44565724

order	32190
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₀₉₅
unambiguous semidirect product	C₃⋊D₅₃₆₅
unambiguous semidirect product	C₅⋊D₃₂₁₉
unambiguous semidirect product	C₂₉⋊D₅₅₅
unambiguous semidirect product	C₃₇⋊D₄₃₅

Splittings

Fitting, socle, derived, Hall	C₃×C₅×C₂₉×C₃₇ ⋊ C₂
Hall	C₅×C₂₉×C₃₇ ⋊ D₃
Hall	C₃×C₂₉×C₃₇ ⋊ D₅
Hall	C₂₉×C₃₇ ⋊ D₁₅
Hall	C₃×C₅×C₃₇ ⋊ D₂₉
Hall	C₃×C₅×C₂₉ ⋊ D₃₇
Hall	C₅×C₃₇ ⋊ D₈₇
Hall	C₅×C₂₉ ⋊ D₁₁₁
Hall	C₃×C₃₇ ⋊ D₁₄₅
Hall	C₃×C₂₉ ⋊ D₁₈₅
Sylow	C₃₇ ⋊ D₄₃₅
Sylow	C₂₉ ⋊ D₅₅₅
Hall	C₃×C₅ ⋊ D₁₀₇₃
Sylow	C₅ ⋊ D₃₂₁₉
Sylow	C₃ ⋊ D₅₃₆₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₂₉×C₃₇	C₂
LCS	G ▷ C₃×C₅×C₂₉×C₃₇
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 74
transitive degree	μ_t(G) = 16095

A minimal faithful permutation representation — 2 generators on 74 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);(2,3)(5,8)(6,7)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(39,74)(40,73)(41,72)(42,71)(43,70)(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(56,57)

Polycyclic presentation:

2,3,5,29,37|b^a=b^2,c^a=c^4,d^a=d^28,e^a=e^36

Conjugacy classes & character table

8049 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₆₀₉₅
maximal normal subgroup of	C₂×D₁₆₀₉₅
maximal quotient of	Dic₁₆₀₉₅, C₂×D₁₆₀₉₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32190, 17);

D16095 #44565724