C₈₃×#9028 #35236852

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₈₃×#9028

Subgroups

	subgroup	G/H
center, socle	C₂³×C₈₃	#120
commutator	C₂²×C₄	C₂²×C₄×C₈₃
Frattini, cosocle	C₂³×C₄	C₂³×C₈₃
prime radical	C₂⁵×C₈₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₃ ◁ C₂³×C₄×C₈₃ ◁ G

696 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 111
transitive degree	μ_t(G) = 5312

A minimal faithful permutation representation — 3 generators on 111 points:

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

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, 2016);