C₁₀₃×#13366 #39918641

order	26368
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₃×#13366

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₀₃	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₀₃
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ C₂×C₄×C₈×C₁₀₃ ◁ G

382 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 147
transitive degree	μ_t(G) = 26368

A minimal faithful permutation representation — 3 generators on 147 points:

(5,6,8,10)(7,11,12,9)(13,14,16,19)(15,23,24,41)(17,29,27,42)(18,32,28,22)(20,36,34,25)(21,38,35,31)(26,43,33,39)(30,40,44,37)(45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147);(1,2)(3,4)(5,7,8,12)(6,9,10,11)(14,19)(20,34)(21,35)(22,32)(23,41)(29,42)(37,40)(39,43);(2,4)(13,15,16,24)(14,20,19,34)(17,30,27,44)(18,33,28,26)(21,39,35,43)(22,40,32,37)(23,42,41,29)(25,38,36,31)

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(26368, 6354);