C₄₃×C₃⋊#1035 #27166355

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

Aliases

direct product	C₄₃×C₃⋊#1035
unambiguous semidirect product	C₃⋊(C₄₃×#1035)

Splittings

Fitting, Hall	C₃×C₂₅×C₄₃ ⋊ C₄
derived, Hall	C₃×C₂₅ ⋊ C₄×C₄₃
Hall	C₂₅×C₄₃ ⋊ Dic₃
Hall	C₃×C₄₃ ⋊ #1035
Sylow	C₂₅ ⋊ Dic₃×C₄₃
Sylow	C₃ ⋊ C₄₃×#1035

Subgroups

	subgroup	G/H
center, hypercenter	C₄₃	C₃⋊#1035
commutator, hypocenter	C₃×C₂₅	C₄×C₄₃
Frattini	C₅	C₄₃×ΓL(1,𝔽₁₆)
Fitting	C₃×C₂₅×C₄₃	C₄
socle	C₃×C₅×C₄₃	AGL(1,𝔽₅)
prime radical	C₃×C₄₃×D₂₅	C₂
cosocle	C₃×D₂₅	C₂×C₄₃
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ 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:

(2,11,5,4)(3,10,9,8)(6,14,16,15)(7,25,20,19)(12,13,21,18)(17,22,23,24)(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);(1,22,18,19,20,10,2,23,4,14,9,21,6,16,12,3,15,11,17,5,8,7,25,13,24)(26,27,28)

Conjugacy classes & character table

1032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 24);

C43×C3⋊#1035 #27166355