C₉×C₄₃×Dic₁₃ #34117404

order	20124
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₉×C₄₃×Dic₁₃

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₉×C₄₃
Hall	C₉×C₁₃×C₄₃ ⋊ C₄
Hall	C₁₃×C₄₃ ⋊ C₄×C₉
Hall	C₉×C₁₃ ⋊ C₄×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₄₃	D₁₃
commutator, hypocenter	C₁₃	C₄×C₉×C₄₃
Frattini	C₂×C₃	C₃×D₁₃×C₄₃
Fitting	C₂×C₉×C₁₃×C₄₃	C₂
socle, prime radical	C₂×C₃×C₁₃×C₄₃	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₄₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₉×C₄₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 20124

A minimal faithful permutation representation — 2 generators on 69 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,17,16,15)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,64,63,65,67,66,68,69);(1,2,4,6,8,10,12,13,11,9,7,5,3)

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, 7);

C9×C43×Dic13 #34117404