C₈₃×#7448 #35235272

order	21248
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₈₃×#7448

Subgroups

	subgroup	G/H
center, socle	C₂×C₈₃	#1361
commutator	C₂×C₁₆	C₂×C₄×C₈₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₈₃
prime radical	C₈₃×#2246	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₃ ◁ C₂×C₄×C₈₃ ◁ C₄×C₈×C₈₃ ◁ C₄×C₁₆×C₈₃ ◁ G

146 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 generators on 115 points:

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

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, 436);