C₈₃×#7837 #35235661

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

Aliases

direct product

C₈₃×#7837

Subgroups

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

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

normal subgroups only

This group has 414 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) = 21248

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

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

Conjugacy classes & character table

3071 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 825);