#97×C₉₇ #15690668

order	3104
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄²×C₉₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

#97×C₉₇

Subgroups

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

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 109
transitive degree	μ_t(G) = 3104

A minimal faithful permutation representation — 2 generators on 109 points:

(5,6,7,10,8,9,11,12)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(1,2,3,4)(6,9)(10,12)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#329×C₉₇, #330×C₉₇, #347×C₉₇, …
maximal normal subgroup of	#329×C₉₇, #330×C₉₇, #347×C₉₇, …
maximal quotient of	#322×C₉₇, #336×C₉₇, #347×C₉₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3104, 4);

#97×C97 #15690668