C₁₆²×C₉₇ #37614017

order	24832
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₆

Aliases

abelian	C₁₆²×C₉₇
multiplicative	(ℤ/26401)ˣ, (ℤ/52802)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈²	C₂²×C₉₇
socle, prime radical	C₂²×C₉₇	C₈²
LCS	G ▷ C₁
UCS	C₁ ◁ G

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 129
transitive degree	μ_t(G) = 24832

A minimal faithful permutation representation — 2 generators on 129 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(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);(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)

Conjugacy classes & character table

24832 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₁₇×C₁₅₅₃
outer automorphism group of	C₁₇×C₁₅₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24832, 39);

C162×C97 #37614017