C₈₃×#8507 #35236331

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

Aliases

direct product

C₈₃×#8507

Subgroups

	subgroup	G/H
center, socle	C₂³×C₈₃	#120
commutator	C₄²	C₂²×C₄×C₈₃
Frattini, cosocle	C₂×C₄²	C₂³×C₈₃
prime radical	C₂²×D₄×C₈₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₃ ◁ C₂×C₄²×C₈₃ ◁ G

736 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 10624

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

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

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, 1495);