C₈₃×#9067 #35236891

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

Aliases

direct product

C₈₃×#9067

Subgroups

	subgroup	G/H
center	C₂×C₄×C₈₃	#120
commutator	C₄²	C₂²×C₄×C₈₃
Frattini, cosocle	C₂×C₄²	C₂³×C₈₃
socle	C₂²×C₈₃	#386
prime radical	#532×C₈₃	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₃ ◁ C₂×C₄²×C₈₃ ◁ G

444 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 10624

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

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

Conjugacy classes & character table

4316 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 2055);