#1039×C₄₃⋊C₃ #27166377

order	12900
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₅

Aliases

direct product

#1039×C₄₃⋊C₃

Splittings

derived, Hall	C₅²×C₄₃ ⋊ C₃×C₄
Hall	C₄₃×#1039 ⋊ C₃
Hall	C₅²×C₄₃⋊C₃ ⋊ C₄
Sylow	C₄₃ ⋊ C₃×#1039
Sylow	C₅² ⋊ C₄×C₄₃⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊D₅×C₄₃⋊C₃
commutator, hypocenter	C₅²×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₅²×C₄₃	C₂×C₃
prime radical	C₂×C₅²×C₄₃⋊C₃	C₂
LCS	G ▷ C₅²×C₄₃
UCS	C₁ ◁ C₂

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 4300

A minimal faithful permutation representation — 3 generators on 57 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 46);

#1039×C43⋊C3 #27166377