C₇₁×#13699 #31834571

order	18176
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₁×#13699

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₇₁
prime radical	C₇₁×#2215	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂²×C₄×C₇₁ ◁ C₂²×C₈×C₇₁ ◁ C₂²×C₁₆×C₇₁ ◁ G

200 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 107
transitive degree	μ_t(G) = 9088

A minimal faithful permutation representation — 3 generators on 107 points:

(1,2)(3,4)(6,11)(7,16)(8,17)(9,20)(12,19)(13,22)(14,30)(15,31)(18,27)(21,34)(23,24)(25,29)(26,35)(28,36)(32,33)(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);(5,6,12,26,8,14,18,25,20,29,33,30,34,35,7,11,10,13,16,24,21,28,32,31,9,15,27,36,17,23,19,22);(2,4)(6,13)(11,22)(14,28)(15,29)(23,35)(24,26)(25,31)(30,36)

Conjugacy classes & character table

3266 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 6687);