#102×C₉₇ #15690673

order	3104
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₉₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#102×C₉₇

Subgroups

	subgroup	G/H
center, socle	C₂²×C₉₇	D₄
commutator	C₄	C₂×C₄×C₉₇
Frattini, cosocle	C₂×C₄	C₂²×C₉₇
prime radical	C₂×D₄×C₉₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉₇ ◁ C₂×C₄×C₉₇ ◁ G

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

1358 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×#102×C₉₇, #416×C₉₇, #417×C₉₇, …
maximal normal subgroup of	C₂×#102×C₉₇, #416×C₉₇, #417×C₉₇, …
maximal quotient of	D₄⋊C₈×C₉₇, #327×C₉₇, #331×C₉₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3104, 9);

#102×C97 #15690673