C₃×C₁₁⋊D₄₀₇ #41001760

order	26862
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁₁

Aliases

direct product	C₃×C₁₁⋊D₄₀₇
unambiguous semidirect product	C₁₁⋊(C₃×D₄₀₇)

Splittings

Fitting, socle, Hall	C₃×C₁₁²×C₃₇ ⋊ C₂
derived, Hall	C₁₁²×C₃₇ ⋊ C₂×C₃
Hall	C₃×C₁₁² ⋊ D₃₇
Sylow	C₁₁² ⋊ C₃×D₃₇
Hall	C₃×C₃₇ ⋊ C₁₁⋊D₁₁
Sylow	C₃₇ ⋊ C₃×C₁₁⋊D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₁₁⋊D₄₀₇
commutator, cosocle, hypocenter	C₁₁²×C₃₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₃₇	C₂
LCS	G ▷ C₁₁²×C₃₇
UCS	C₁ ◁ C₃

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 13431

A minimal faithful permutation representation — 3 generators on 62 points:

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

Conjugacy classes & character table

6720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26862, 34);

C3×C11⋊D407 #41001760