C₁₃⋊C₃×Dic₈₃ #27188271

order	12948
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

derived, Hall	C₁₃×C₈₃ ⋊ C₃×C₄
Hall	C₁₃×Dic₈₃ ⋊ C₃
Hall	C₁₃⋊C₃×C₈₃ ⋊ C₄
Sylow	C₈₃ ⋊ C₄×C₁₃⋊C₃
Sylow	C₁₃ ⋊ C₃×Dic₈₃

Subgroups

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

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)(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)(85,86,88)(87,90,93)(89,92,91)(94,96,95)(97,100,99,98);(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)(84,85,87,86,89,93,90,94,96,88,91,95,92)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12948, 10);

C13⋊C3×Dic83 #27188271