C₃×C₅²×Dic₄₃ #27166389

order	12900
isoclinism	isoclinic class of D₄₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product

C₃×C₅²×Dic₄₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²	D₄₃
commutator, hypocenter	C₄₃	C₃×C₄×C₅²
Frattini	C₂	C₃×C₅²×D₄₃
Fitting, socle, prime radical	C₂×C₃×C₅²×C₄₃	C₂
cosocle	C₂×C₄₃	C₂×C₃×C₅²
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂×C₃×C₅²

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 — 2 generators on 60 points:

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

Conjugacy classes & character table

3450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 58);

C3×C52×Dic43 #27166389