C₈₃×C₃⋊#261 #27188285

order	12948
isoclinism	isoclinic class of C₃⋊#261
automorphism	?
homology	Abelianization (H₁) = C₄×C₈₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₈₃×C₃⋊#261
unambiguous semidirect product	C₃⋊(#261×C₈₃)

Splittings

Fitting, socle, Hall	C₃×C₁₃×C₈₃ ⋊ C₄
derived, Hall	C₃×C₁₃ ⋊ C₄×C₈₃
Hall	C₁₃×C₈₃ ⋊ Dic₃
Hall	C₃×C₈₃ ⋊ #261
Sylow	C₁₃ ⋊ Dic₃×C₈₃
Sylow	C₃ ⋊ #261×C₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₈₃	C₃⋊#261
commutator, hypocenter	C₃×C₁₃	C₄×C₈₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₈₃	C₄
prime radical	C₃×D₁₃×C₈₃	C₂
cosocle	C₃×D₁₃	C₂×C₈₃
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₈₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 99
transitive degree	μ_t(G) = 3237

A minimal faithful permutation representation — 2 generators on 99 points:

(2,6,4,3)(5,10,9,8)(7,11,13,12)(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);(1,2,5,10,12,3,7,13,6,11,8,9,4)(14,15,16)

Conjugacy classes & character table

1245 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12948, 24);

C83×C3⋊#261 #27188285