C₈₃×#11456 #35239280

order	21248
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₈₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₈₃×#11456

Subgroups

	subgroup	G/H
center	C₄×C₈₃	C₂×#99
commutator	C₂×C₄	C₂²×C₈×C₈₃
Frattini, cosocle	C₂×M₁₆	C₂³×C₈₃
socle	C₂×C₈₃	C₂×#324
prime radical	C₂⁴×C₈₃	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈₃ ◁ C₂²×C₄×C₈₃ ◁ C₂²×M₁₆×C₈₃ ◁ G

364 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 138 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 — 3 generators on 115 points:

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

Conjugacy classes & character table

3818 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 4444);