#2402×C₁₄₉ #34041315

order	19072
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₄₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

#2402×C₁₄₉

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₄₉	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₄₉
socle, prime radical	C₂³×C₁₄₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₄₉ ◁ G

400 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 173
transitive degree	μ_t(G) = 19072

A minimal faithful permutation representation — 4 generators on 173 points:

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

Conjugacy classes & character table

6556 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₄₉×#10372, C₁₄₉×#10373
maximal normal subgroup of	C₁₄₉×#10372, C₁₄₉×#10373
maximal quotient of	C₁₄₉×#13846, C₁₄₉×#13848, C₁₄₉×#13854, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 1134);