C₃×C₁₇⋊(C₁₉⋊D₁₉) #49145661

order	36822
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁₉

Aliases

direct product	C₃×C₁₇⋊(C₁₉⋊D₁₉)
unambiguous semidirect product	C₁₇⋊(C₃×C₁₉⋊D₁₉)

Splittings

Fitting, socle, Hall	C₃×C₁₇×C₁₉² ⋊ C₂
derived, Hall	C₁₇×C₁₉² ⋊ C₂×C₃
Hall	C₃×C₁₉² ⋊ D₁₇
Sylow	C₁₉² ⋊ C₃×D₁₇
Hall	C₃×C₁₇ ⋊ C₁₉⋊D₁₉
Sylow	C₁₇ ⋊ C₃×C₁₉⋊D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₁₇⋊(C₁₉⋊D₁₉)
commutator, cosocle, hypocenter	C₁₇×C₁₉²	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₁₉²	C₂
LCS	G ▷ C₁₇×C₁₉²
UCS	C₁ ◁ C₃

176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 18411

A minimal faithful permutation representation — 3 generators on 58 points:

(1,2,3)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58);(4,5,7,9,11,13,15,17,19,20,18,16,14,12,10,8,6)(40,41,43,45,47,49,51,53,55,57,58,56,54,52,50,48,46,44,42);(21,22,24,26,28,30,32,34,36,38,39,37,35,33,31,29,27,25,23)

Conjugacy classes & character table

9210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36822, 40);

C3×C17⋊(C19⋊D19) #49145661