C₃⋊Dic₃×C₁₀₇ #16838709

order	3852
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₀₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃⋊Dic₃×C₁₀₇
unambiguous semidirect product	C₃⋊(Dic₃×C₁₀₇)

Splittings

derived, Sylow	C₃² ⋊ C₄×C₁₀₇
Hall	C₃²×C₁₀₇ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₀₇	C₃⋊D₃
commutator, hypocenter	C₃²	C₄×C₁₀₇
Frattini	C₂	C₃⋊D₃×C₁₀₇
Fitting, socle, prime radical	C₂×C₃²×C₁₀₇	C₂
cosocle	C₂×C₃²	C₂×C₁₀₇
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₀₇

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 117
transitive degree	μ_t(G) = 3852

A minimal faithful permutation representation — 3 generators on 117 points:

(1,2,3,4)(6,7)(9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117);(8,9,10);(5,6,7)

Conjugacy classes & character table

1284 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₃⋊Dic₃×C₁₀₇, C₁₀₇×C₃⋊Dic₁₅, C₁₀₇×C₃⋊ΓL(1,𝔽₁₆), …
maximal normal subgroup of	C₅×C₃⋊Dic₃×C₁₀₇, C₇×C₃⋊Dic₃×C₁₀₇
maximal quotient of	C₅×C₃⋊Dic₃×C₁₀₇, C₁₀₇×C₃⋊Dic₁₅, C₁₀₇×C₃⋊ΓL(1,𝔽₁₆), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3852, 15);

C3⋊Dic3×C107 #16838709