D₃×#20259721 #49149555

order	36972
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

D₃×#20259721

Splittings

Fitting, socle, derived	C₃×C₁₃×C₇₉ ⋊ C₂²×C₃
Hall	C₃×#15690493 ⋊ C₂²
Hall	C₁₃×C₇₉ ⋊ C₂×C₃×D₃
Sylow	C₇₉ ⋊ D₃×D₁₃⋊C₃
Sylow	C₁₃ ⋊ D₃×D₇₉⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₇₉	C₂²×C₃
LCS	G ▷ C₃×C₁₃×C₇₉
UCS	C₁

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 3081

A minimal faithful permutation representation — 2 generators on 95 points:

(1,2,3)(5,9,10,6,7,11)(8,15,14,12,13,16)(18,22,23,19,20,24)(21,30,31,25,26,40)(27,43,44,33,34,57)(28,42,38,36,32,29)(35,62,63,46,47,79)(37,60,61,49,45,54)(39,41,59,51,52,55)(48,83,84,65,66,94)(50,82,67,68,64,76)(53,58,81,70,71,77)(56,90,89,74,75,73)(69,95,87,86,85,92)(72,80,91,88,78,93);(2,3)(4,5,8,7,11,14,13,15,16,10,9,12,6)(17,18,21,27,35,48,67,44,59,60,43,58,78,47,64,75,77,79,92,86,68,49,36,20,24,29,39,53,72,89,61,31,42,30,41,56,66,85,84,91,93,94,95,83,74,52,26,32,40,54,73,88,70,51,38,23,22,28,37,50,69,87,63,81,90,82,62,80,71,34,45,55,57,76,65,46,33,25,19)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 203);

D3×#20259721 #49149555