C₃×D₂₅×D₄₃ #27166353

order	12900
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃×D₂₅×D₄₃

Splittings

Fitting, Hall	C₃×C₂₅×C₄₃ ⋊ C₂²
derived, Hall	C₂₅×C₄₃ ⋊ C₂²×C₃
Hall	C₃×C₄₃ ⋊ C₂×D₂₅
Hall	C₃×C₂₅ ⋊ C₂×D₄₃
Sylow	C₄₃ ⋊ C₂×C₃×D₂₅
Sylow	C₂₅ ⋊ C₂×C₃×D₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₂₅×D₄₃
commutator, cosocle, hypocenter	C₂₅×C₄₃	C₂²×C₃
Frattini	C₅	C₃×D₅×D₄₃
Fitting	C₃×C₂₅×C₄₃	C₂²
socle	C₃×C₅×C₄₃	C₂×D₅
LCS	G ▷ C₂₅×C₄₃
UCS	C₁ ◁ C₃

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:

(2,3)(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)(44,49,64,63,47,46,57,67,53,52,51,66,61,54,60,59,58,48,62,65,50,45,55,68,56)(69,70,71);(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)(45,47)(46,50)(48,53)(49,56)(51,59)(52,58)(54,61)(55,63)(57,65)(60,66)(62,67)(64,68)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 22);

C3×D25×D43 #27166353