C₉₇×#1375 #27137333

order	12416
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₉₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₉₇×#1375

Subgroups

	subgroup	G/H
center	C₂×C₄×C₉₇	C₄²
commutator	C₄	C₄×C₈×C₉₇
Frattini, cosocle	C₂²×C₈	C₂²×C₉₇
socle	C₂²×C₉₇	#97
prime radical	C₂³×C₉₇	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉₇ ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 117
transitive degree	μ_t(G) = 3104

A minimal faithful permutation representation — 2 generators on 117 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉₇×#7109
maximal normal subgroup of	C₉₇×#7109

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12416, 107);

C97×#1375 #27137333