C₃×C₄₁⋊#64425 #49116352

order	36162
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃×C₇

Aliases

direct product	C₃×C₄₁⋊#64425
unambiguous semidirect product	C₄₁⋊(C₃×#64425)

Splittings

Fitting, socle	C₃×C₇²×C₄₁ ⋊ C₂×C₃
derived, Hall	C₇²×C₄₁ ⋊ C₂×C₃²
Hall	C₃×C₄₁×#3862 ⋊ C₂
Hall	C₇⋊D₂₈₇ ⋊ C₃²
Hall	C₃×#3862 ⋊ D₄₁
Sylow	C₇² ⋊ C₃²×D₄₁
Sylow	C₄₁ ⋊ C₃×#64425

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₄₁⋊#64425
commutator, cosocle, hypocenter	C₇²×C₄₁	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₄₁	C₂×C₃
LCS	G ▷ C₇²×C₄₁
UCS	C₁ ◁ C₃

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 2583

A minimal faithful permutation representation — 2 generators on 58 points:

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

Conjugacy classes & character table

1182 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36162, 94);

C3×C41⋊#64425 #49116352