C₉₇×#1327 #27137285

order	12416
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₉₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₉₇×#1327

Subgroups

	subgroup	G/H
center	C₄×C₉₇	#99
commutator	C₂×C₄	C₂×C₈×C₉₇
Frattini, cosocle	C₂×M₁₆	C₂²×C₉₇
socle	C₂×C₉₇	#324
prime radical	C₂³×C₉₇	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₉₇ ◁ C₂×C₄×C₉₇ ◁ C₂×M₁₆×C₉₇ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 113
transitive degree	μ_t(G) = 1552

A minimal faithful permutation representation — 2 generators on 113 points:

(1,2,4,9,5,8,13,15,6,10,12,16,3,7,11,14)(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);(2,7,10,8)(4,12)(9,14,16,15)(11,13)

Conjugacy classes & character table

2522 conjugacy classes. The character table is too large to display.

Relationships

maximal quotient of

C₉₇×#7062, C₉₇×#7063, C₉₇×#7067

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12416, 59);

C97×#1327 #27137285