C₂×D₃×C₂₅×C₄₃ #27166368

order	12900
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₅×C₄₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₃×C₂₅×C₄₃
unambiguous semidirect product	C₃⋊(C₂²×C₂₅×C₄₃)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₂₅×C₄₃)

Splittings

Fitting	C₂×C₃×C₂₅×C₄₃ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂²×C₂₅×C₄₃
Hall	C₃×C₂₅×C₄₃ ⋊ C₂²
Hall	C₃×C₄₃ ⋊ C₂²×C₂₅
Hall	C₃×C₂₅ ⋊ C₂²×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₅×C₄₃	D₃
commutator, hypocenter	C₃	C₂²×C₂₅×C₄₃
Frattini	C₅	C₂×C₅×D₃×C₄₃
Fitting	C₂×C₃×C₂₅×C₄₃	C₂
socle	C₂×C₃×C₅×C₄₃	C₂×C₅
prime radical	C₂×C₅×D₃×C₄₃	C₅
cosocle	C₃×C₅	C₂²×C₅×C₄₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₂₅×C₄₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 6450

A minimal faithful permutation representation — 2 generators on 73 points:

(2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46)(47,51,59,67,71,49,55,64,70,57,52,60,68,53,62,56,65,50,58,66,61,48,54,63,69);(1,2,3)(72,73)

Conjugacy classes & character table

6450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 37);

C2×D3×C25×C43 #27166368