C₂×#1663×C₁₄₉ #49197938

order	38144
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₄₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×#1663×C₁₄₉

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₄₉	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₄₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₄₉ ◁ C₂×C₄²×C₁₄₉ ◁ G

830 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 238 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) = 183
transitive degree	μ_t(G) = 38144

A minimal faithful permutation representation — 4 generators on 183 points:

(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183);(3,4,9,13)(5,14,16,17)(6,15,10,18)(7,12,8,11)(19,20,24,22)(21,27,30,34)(23,31,33,26)(25,32,28,29);(3,5)(4,10)(6,13)(7,18)(8,15)(9,16)(11,17)(12,14)(19,21,24,30)(20,25,22,28)(23,32,33,29)(26,34,31,27);(3,6,9,10)(4,5,13,16)(7,17,8,14)(11,15,12,18)(19,22,24,20)(21,28,30,25)(23,26,33,31)(27,32,34,29)

Conjugacy classes & character table

5960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38144, 11977);