C₈₃×#10379 #35238203

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₈₃×#10379

Subgroups

	subgroup	G/H
center, socle	C₂²×C₈₃	#393
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₈₃
prime radical	C₂³×C₈₃	#120
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂×C₄²×C₈₃ ◁ G

360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 115
transitive degree	μ_t(G) = 2656

A minimal faithful permutation representation — 3 generators on 115 points:

(2,7,9,21)(3,11)(4,16)(8,25,17,20)(10,24,22,12)(14,30)(15,28)(18,19)(23,26,29,32)(27,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(2,8,9,17)(3,11)(7,20,21,25)(10,26,22,32)(12,29,24,23)(14,27)(15,28)(30,31);(1,2,6,10)(3,12,11,21)(4,17,19,32)(5,9,13,22)(7,15,24,28)(8,16,26,18)(14,20,27,23)(25,31,29,30)

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, 3367);