C₃×C₄₃×#1039 #27166392

order	12900
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₄₃ · Schur multiplier (H₂) = C₅

Aliases

direct product

C₃×C₄₃×#1039

Splittings

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

Subgroups

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

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 12900

A minimal faithful permutation representation — 3 generators on 60 points:

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

Conjugacy classes & character table

3612 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 61);

C3×C43×#1039 #27166392