C₈₃×#13049 #35240873

order	21248
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₈₃×#13049

Subgroups

	subgroup	G/H
center, socle	C₂²×C₈₃	B(4,𝔽₂)
commutator	C₂×D₄	C₂²×C₄×C₈₃
Frattini, cosocle	C₂²×D₄	C₂³×C₈₃
prime radical	C₂×#453×C₈₃	C₂
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂³×C₈₃ ◁ C₂²×D₄×C₈₃ ◁ G

796 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 796 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 103
transitive degree	μ_t(G) = 2656

A minimal faithful permutation representation — 3 generators on 103 points:

(2,4)(5,6)(7,10)(8,12,17,11)(9,13)(14,19)(15,18,16,20)(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);(1,2,3,4)(5,7)(6,10)(8,16)(9,14)(11,20)(12,18)(13,19)(15,17);(6,11)(7,14)(8,17)(10,18)(12,13)(19,20)

Conjugacy classes & character table

2822 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 6037);