C₉₇×#1707 #27137665

order	12416
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₉₇×#1707

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₉₇	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₉₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉₇ ◁ C₄²×C₉₇ ◁ G

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 12416

A minimal faithful permutation representation — 3 generators on 121 points:

(2,5)(3,7)(6,8)(9,10,13,16)(11,17,20,24)(12,21,18,15)(14,22,23,19)(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);(9,11,18,22,13,20,12,19)(10,14,21,24,16,23,15,17);(1,2,3,5,4,6,7,8)

Conjugacy classes & character table

3686 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉₇×#7095
maximal normal subgroup of	C₉₇×#7095

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12416, 439);

C97×#1707 #27137665