C₈₃×#12873 #35240697

order	21248
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₈₃×#12873

Subgroups

	subgroup	G/H
center, socle	C₂×C₈₃	#1823
commutator	C₂×C₈	C₂²×C₄×C₈₃
Frattini, cosocle	C₂²×C₈	C₂³×C₈₃
prime radical	C₂×#41×C₈₃	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₃ ◁ C₂²×C₄×C₈₃ ◁ C₂×#131×C₈₃ ◁ G

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

normal subgroups only

This group has 380 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)(3,12,14,7)(4,16)(5,20)(6,9)(8,13,25,30)(10,18)(11,22)(15,24,21,28)(17,26,31,23)(19,29)(27,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(1,3)(2,7)(4,13)(5,15)(6,14)(8,16)(9,12)(10,23)(11,24)(17,18)(19,30)(20,28)(21,22)(25,29)(26,27)(31,32);(1,3)(2,8,9,25)(4,17)(5,21)(6,14)(7,16,12,29)(10,28,27,24)(11,23,20,26)(13,18)(15,22)(19,31)(30,32)

Conjugacy classes & character table

3320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 5861);