#1473×C₁₉₃ #37591090

order	24704
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

#1473×C₁₉₃

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₁₉₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉₃
prime radical	C₂⁴×C₁₉₃	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉₃ ◁ C₂×C₄²×C₁₉₃ ◁ G

214 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 88 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) = 225
transitive degree	μ_t(G) = 6176

A minimal faithful permutation representation — 3 generators on 225 points:

(1,2,4,9,6,10,16,23)(3,8,13,21,11,22,24,32)(5,7,15,18,12,19,26,30)(14,17,28,29,25,20,27,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225);(2,7)(3,11)(4,15)(8,20)(10,19)(13,27)(14,25)(16,26)(17,22)(21,32)(24,28)(29,31);(1,3,12,25)(2,8,19,20)(4,13,26,27)(5,14,6,11)(7,17,10,22)(9,21,30,31)(15,28,16,24)(18,29,23,32)

Conjugacy classes & character table

6176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24704, 205);