C₃×C₁₃×Dic₈₃ #27188264

order	12948
isoclinism	isoclinic class of D₈₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₃×Dic₈₃
unambiguous semidirect product	C₈₃⋊(C₃×C₄×C₁₃)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₈₃
commutator, hypocenter	C₈₃	C₃×C₄×C₁₃
Frattini	C₂	C₃×C₁₃×D₈₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₈₃	C₂
cosocle	C₂×C₈₃	C₂×C₃×C₁₃
LCS	G ▷ C₈₃
UCS	C₁ ◁ C₂×C₃×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 103
transitive degree	μ_t(G) = 12948

A minimal faithful permutation representation — 2 generators on 103 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)(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)(84,87,86,85)(88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)

Conjugacy classes & character table

3354 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12948, 3);

C3×C13×Dic83 #27188264