C₈₃×#7364 #35235188

order	21248
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₈₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₈₃×#7364

Subgroups

	subgroup	G/H
center	C₈×C₈₃	#99
commutator	C₂×C₄	C₂×C₁₆×C₈₃
Frattini, cosocle	C₂×M₃₂	C₂²×C₈₃
socle	C₂×C₈₃	#1322
prime radical	C₂³×C₈₃	M₃₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₈₃ ◁ C₂×C₈×C₈₃ ◁ C₂×M₃₂×C₈₃ ◁ G

126 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 54 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:

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

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, 352);