Dic₃×#15690493 #49149482

order	36972
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×#15690493
unambiguous semidirect product	C₃⋊(C₄×#15690493)

Splittings

derived	C₃×C₁₃×C₇₉ ⋊ C₃×C₄
Hall	C₃×#15690493 ⋊ C₄
Hall	C₁₃×C₇₉ ⋊ C₃×Dic₃
Sylow	C₇₉ ⋊ Dic₃×C₁₃⋊C₃
Sylow	C₁₃ ⋊ Dic₃×C₇₉⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×#15690493
commutator, hypocenter	C₃×C₁₃×C₇₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₃×C₇₉	C₂×C₃
prime radical	C₂×C₃×#15690493	C₂
LCS	G ▷ C₃×C₁₃×C₇₉
UCS	C₁ ◁ C₂

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 99
transitive degree	μ_t(G) = 12324

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

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

Conjugacy classes & character table

2070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 130);

Dic3×#15690493 #49149482