C₈₃×#10098 #35237922

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₈₃×#10098

Subgroups

	subgroup	G/H
center, socle	C₂²×C₈₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₈₃
prime radical	C₂²×D₄×C₈₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂×C₄²×C₈₃ ◁ G

512 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 102 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:

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

Conjugacy classes & character table

2573 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 3086);