C₂×#1424×C₁₅₁ #50318557

order	38656
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₅₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×#1424×C₁₅₁

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₅₁	D₁₆
commutator	C₁₆	C₂²×C₄×C₁₅₁
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₅₁
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ C₂²×C₄×C₁₅₁ ◁ C₂²×C₈×C₁₅₁ ◁ C₂²×C₁₆×C₁₅₁ ◁ G

206 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 189
transitive degree	μ_t(G) = 38656

A minimal faithful permutation representation — 3 generators on 189 points:

(1,2)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189);(3,4,5,6)(8,13)(9,18)(10,19)(11,22)(14,21)(15,30)(16,33)(17,27)(20,29)(23,36)(24,25)(26,31)(28,37)(32,38)(34,35);(7,8,14,28,10,15,20,26,22,31,35,30,36,37,9,13,12,17,18,25,23,32,34,33,11,16,29,38,19,24,21,27)

Conjugacy classes & character table

11476 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38656, 6620);