C₈₃×#10369 #35238193

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₈₃×#10369

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

364 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 5312

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

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

Conjugacy classes & character table

3320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 3357);