C₈₃×#11757 #35239581

order	21248
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₈₃×#11757

Subgroups

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₈₃
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₈₃
prime radical	C₈₃×#2539	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂⁴×C₈₃ ◁ C₂²×C₂²⋊C₄×C₈₃ ◁ G

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

normal subgroups only

This group has 700 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) = 99
transitive degree	μ_t(G) = 2656

A minimal faithful permutation representation — 3 generators on 99 points:

(2,5,6,7)(9,10)(11,14,16,13)(12,15)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,2)(3,7)(4,6)(5,8)(10,13)(11,16)(14,15);(11,16)(13,14)

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, 4745);