C₁₀₃×C₇⋊Dic₇ #34118232

order	20188
isoclinism	isoclinic class of C₇⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₀₃ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₁₀₃×C₇⋊Dic₇
unambiguous semidirect product	C₇⋊(Dic₇×C₁₀₃)

Splittings

derived, Sylow	C₇² ⋊ C₄×C₁₀₃
Hall	C₇²×C₁₀₃ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₀₃	C₇⋊D₇
commutator, hypocenter	C₇²	C₄×C₁₀₃
Frattini	C₂	C₇⋊D₇×C₁₀₃
Fitting, socle, prime radical	C₂×C₇²×C₁₀₃	C₂
cosocle	C₂×C₇²	C₂×C₁₀₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₁₀₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 20188

A minimal faithful permutation representation — 3 generators on 121 points:

(1,4,3,2)(6,7)(8,9)(10,11)(13,14)(15,16)(17,18)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121);(12,13,15,17,18,16,14);(5,6,8,10,11,9,7)

Conjugacy classes & character table

5356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20188, 12);

C103×C7⋊Dic7 #34118232