C₈₃×#12139 #35239963

order	21248
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₈₃×#12139

Subgroups

	subgroup	G/H
center, socle	C₂²×C₈₃	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₈₃
prime radical	#534×C₈₃	C₂²
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂³×C₈₃ ◁ C₂×C₂²⋊C₄×C₈₃ ◁ G

404 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 5312

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

(2,6)(3,4)(7,8)(9,10)(11,17)(12,20)(13,16)(14,19)(15,22)(18,24)(21,23)(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);(1,2)(3,6)(4,8)(5,7)(9,11,13,18)(10,14,16,23)(12,21,22,19)(15,24,20,17);(1,3,5,4)(2,6,7,8)(11,18)(12,22)(14,23)(17,24)

Conjugacy classes & character table

2075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 5127);