C₃×C₄₃⋊#1035 #27166352

order	12900
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₄₃⋊#1035

Splittings

Fitting, Hall	C₃×C₂₅×C₄₃ ⋊ C₄
derived, Hall	C₂₅×C₄₃ ⋊ C₃×C₄
Hall	C₃×C₄₃ ⋊ #1035
Hall	C₃×C₂₅ ⋊ Dic₄₃
Sylow	C₄₃ ⋊ C₃×#1035
Sylow	C₂₅ ⋊ C₃×Dic₄₃

Subgroups

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

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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 21);

C3×C43⋊#1035 #27166352