C₄×C₅²×C₁₆₃ #30654389

order	16300
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅

Aliases

abelian

C₄×C₅²×C₁₆₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₅²×C₁₆₃
socle, prime radical	C₂×C₅²×C₁₆₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 177
transitive degree	μ_t(G) = 16300

A minimal faithful permutation representation — 2 generators on 177 points:

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

Conjugacy classes & character table

16300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅²×C₈×C₁₆₃, C₂×C₄×C₅²×C₁₆₃
maximal normal subgroup of	C₅²×C₈×C₁₆₃, C₂×C₄×C₅²×C₁₆₃
maximal quotient of	C₅²×C₈×C₁₆₃, C₂×C₄×C₅²×C₁₆₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16300, 12);

C4×C52×C163 #30654389