C₄×C₁₃⋊C₃×C₈₃ #27188263

order	12948
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₈₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄×C₁₃⋊C₃×C₈₃
unambiguous semidirect product	(C₄×C₁₃)⋊(C₃×C₈₃)
unambiguous semidirect product	(C₄×C₁₃×C₈₃)⋊C₃

Splittings

Fitting, Hall	C₄×C₁₃×C₈₃ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₃×C₄×C₈₃
Hall	C₁₃×C₈₃ ⋊ C₃×C₄
Hall	C₄×C₁₃ ⋊ C₃×C₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₈₃	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₃×C₄×C₈₃
Frattini	C₂	C₂×C₁₃⋊C₃×C₈₃
Fitting	C₄×C₁₃×C₈₃	C₃
socle	C₂×C₁₃×C₈₃	C₂×C₃
prime radical	C₂×C₁₃⋊C₃×C₈₃	C₂
cosocle	C₂×C₁₃	C₂×C₃×C₈₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₄×C₈₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 100
transitive degree	μ_t(G) = 4316

A minimal faithful permutation representation — 2 generators on 100 points:

(2,3,5)(4,7,10)(6,9,8)(11,13,12)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96)(97,98,99,100);(1,2,4,3,6,10,7,11,13,5,8,12,9)

Conjugacy classes & character table

2324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12948, 2);

C4×C13⋊C3×C83 #27188263