Dic₃×#14584115 #45691933

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×#14584115
unambiguous semidirect product	C₃⋊(C₄×#14584115)

Splittings

derived	C₃×C₇²×C₁₉ ⋊ C₃×C₄
Hall	C₃×#14584115 ⋊ C₄
Hall	C₇²×C₁₉ ⋊ C₃×Dic₃
Sylow	C₇² ⋊ Dic₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ Dic₃×#3861

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×#14584115
commutator, hypocenter	C₃×C₇²×C₁₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×#14584115	C₂
LCS	G ▷ C₃×C₇²×C₁₉
UCS	C₁ ◁ C₂

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 11172

A minimal faithful permutation representation — 3 generators on 40 points:

(2,3)(4,5,6,7)(9,10,11)(12,14,13)(16,17,18)(19,21,20)(23,24,26)(25,28,29)(27,31,30)(32,36,34)(33,37,35)(38,40,39);(1,2,3)(15,16,17,19,18,20,21)(22,23,25,29,34,39,36,24,27,32,37,26,30,35,28,33,38,40,31);(8,9,10,12,11,13,14)

Conjugacy classes & character table

1878 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 731);

Dic3×#14584115 #45691933