C₉₇×#1313 #27137271

order	12416
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₉₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₉₇×#1313

Subgroups

	subgroup	G/H
center	C₂×C₄×C₉₇	C₄²
commutator	C₄	C₄×C₈×C₉₇
Frattini, cosocle	C₄×C₈	C₂²×C₉₇
socle, prime radical	C₂²×C₉₇	#97
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉₇ ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 121 points:

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

Conjugacy classes & character table

4268 conjugacy classes. The character table is too large to display.

Relationships

maximal quotient of

C₉₇×#7053

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12416, 45);

C97×#1313 #27137271