D₃×C₄₃×D₂₅ #27166358

order	12900
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₄₃×D₂₅
unambiguous semidirect product	(D₃×C₂₅)⋊(C₂×C₄₃)
unambiguous semidirect product	(C₃×D₂₅)⋊(C₂×C₄₃)
unambiguous semidirect product	D₇₅⋊(C₂×C₄₃)

Splittings

Fitting, Hall	C₃×C₂₅×C₄₃ ⋊ C₂²
derived, Hall	C₃×C₂₅ ⋊ C₂²×C₄₃
Hall	C₂₅×C₄₃ ⋊ C₂×D₃
Hall	C₃×C₄₃ ⋊ C₂×D₂₅
Sylow	C₂₅ ⋊ C₂×D₃×C₄₃
Sylow	C₃ ⋊ C₂×C₄₃×D₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₄₃	D₃×D₂₅
commutator, cosocle, hypocenter	C₃×C₂₅	C₂²×C₄₃
Frattini	C₅	D₃×D₅×C₄₃
Fitting	C₃×C₂₅×C₄₃	C₂²
socle	C₃×C₅×C₄₃	C₂×D₅
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ C₄₃

60 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)(3,7)(5,10)(6,13)(8,16)(9,15)(11,18)(12,20)(14,22)(17,23)(19,24)(21,25)(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);(1,14,18,19,13,3,23,5,25,4,8,15,12,20,9,16,2,21,10,17,7,6,24,11,22)(27,28)

Conjugacy classes & character table

1806 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 27);

D3×C43×D25 #27166358