#117×C₉₇ #15690688

order	3104
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₉₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

#117×C₉₇

Subgroups

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

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 109
transitive degree	μ_t(G) = 1552

A minimal faithful permutation representation — 3 generators on 109 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	H(3,ℤ/4)×C₉₇, #339×C₉₇, #344×C₉₇, …
maximal normal subgroup of	H(3,ℤ/4)×C₉₇, #339×C₉₇, #344×C₉₇, …
maximal quotient of	#376×C₉₇, C₄×C₂²⋊C₄×C₉₇, C₄×C₄⋊C₄×C₉₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3104, 24);

#117×C97 #15690688