C₂×D₃₉×C₈₃ #27188296

order	12948
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₃₉×C₈₃
unambiguous semidirect product	(C₂×C₃)⋊(D₁₃×C₈₃)
unambiguous semidirect product	(C₂×C₁₃)⋊(D₃×C₈₃)

Splittings

Fitting, socle	C₂×C₃×C₁₃×C₈₃ ⋊ C₂
derived, Hall	C₃×C₁₃ ⋊ C₂²×C₈₃
Hall	C₃×C₁₃×C₈₃ ⋊ C₂²
Hall	C₁₃×C₈₃ ⋊ C₂×D₃
Hall	C₃×C₈₃ ⋊ C₂×D₁₃
Sylow	C₁₃ ⋊ C₂×D₃×C₈₃
Sylow	C₃ ⋊ C₂×D₁₃×C₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₈₃	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂²×C₈₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₈₃	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₈₃

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 101
transitive degree	μ_t(G) = 6474

A minimal faithful permutation representation — 2 generators on 101 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(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);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,16)(100,101)

Conjugacy classes & character table

3486 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12948, 35);

C2×D39×C83 #27188296