#131×C₉₇ #15690702

order	3104
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₉₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#131×C₉₇

Subgroups

	subgroup	G/H
center	C₈×C₉₇	C₂²
commutator	C₂	C₂²×C₄×C₉₇
Frattini, cosocle	C₄	C₂³×C₉₇
socle	C₂×C₉₇	C₂²×C₄
prime radical	#41×C₉₇	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₉₇ ◁ G

62 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 113 points:

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

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#350×C₉₇, #443×C₉₇, #444×C₉₇, …
maximal normal subgroup of	#350×C₉₇, #443×C₉₇, #444×C₉₇, …
maximal quotient of	#405×C₉₇, #408×C₉₇, #424×C₉₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3104, 38);

#131×C97 #15690702