C₈₃×#11312 #35239136

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₈₃×#11312

Subgroups

	subgroup	G/H
center, socle	C₂²×C₈₃	#396
commutator	C₂²×C₄	C₂²×C₄×C₈₃
Frattini, cosocle	C₂³×C₄	C₂³×C₈₃
prime radical	C₂⁴×C₈₃	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂³×C₄×C₈₃ ◁ G

538 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 206 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) = 103
transitive degree	μ_t(G) = 5312

A minimal faithful permutation representation — 3 generators on 103 points:

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

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, 4300);