C₂×C₉×D₁₃×C₄₃ #34117472

order	20124
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₄₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂×C₉×D₁₃×C₄₃

Splittings

Fitting	C₂×C₉×C₁₃×C₄₃ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂²×C₉×C₄₃
Hall	C₉×C₁₃×C₄₃ ⋊ C₂²
Hall	C₁₃×C₄₃ ⋊ C₂²×C₉
Hall	C₉×C₁₃ ⋊ C₂²×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₄₃	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₉×C₄₃
Frattini	C₃	C₂×C₃×D₁₃×C₄₃
Fitting	C₂×C₉×C₁₃×C₄₃	C₂
socle	C₂×C₃×C₁₃×C₄₃	C₂×C₃
prime radical	C₂×C₃×D₁₃×C₄₃	C₃
cosocle	C₃×C₁₃	C₂²×C₃×C₄₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₉×C₄₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 10062

A minimal faithful permutation representation — 2 generators on 67 points:

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

Conjugacy classes & character table

6192 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20124, 75);

C2×C9×D13×C43 #34117472