C₃×C₄₃×#1035 #27166351

order	12900
isoclinism	isoclinic class of #1035
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₄₃×#1035

Splittings

Fitting, Hall	C₃×C₂₅×C₄₃ ⋊ C₄
derived, Sylow	C₂₅ ⋊ C₃×C₄×C₄₃
Hall	C₂₅×C₄₃ ⋊ C₃×C₄
Hall	C₃×C₂₅ ⋊ C₄×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₃	#1035
commutator, hypocenter	C₂₅	C₃×C₄×C₄₃
Frattini	C₅	C₃×AGL(1,𝔽₅)×C₄₃
Fitting	C₃×C₂₅×C₄₃	C₄
socle	C₃×C₅×C₄₃	AGL(1,𝔽₅)
prime radical	C₃×C₄₃×D₂₅	C₂
cosocle	D₂₅	C₂×C₃×C₄₃
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃×C₄₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 3225

A minimal faithful permutation representation — 2 generators on 71 points:

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

Conjugacy classes & character table

1290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 20);

C3×C43×#1035 #27166351