D₃×#16861551 #37590261

order	24642
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#16861551
unambiguous semidirect product	C₃⋊(C₂×#16861551)

Splittings

Fitting, socle, derived	C₃×C₃₇² ⋊ C₂×C₃
Hall	C₃×#16861551 ⋊ C₂
Sylow	C₃₇² ⋊ C₃×D₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₇²	C₂×C₃
LCS	G ▷ C₃×C₃₇²
UCS	C₁

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 4107

A minimal faithful permutation representation — 3 generators on 77 points:

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

Conjugacy classes & character table

1377 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24642, 81);

D3×#16861551 #37590261