C₇₉×#13448 #34125137

order	20224
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₇₉×#13448

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₉
prime radical	C₂²×D₁₆×C₇₉	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ C₂×C₄×C₈×C₇₉ ◁ G

482 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 10112

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

(1,2)(3,4)(10,16)(11,19)(12,13)(14,22)(17,24)(18,21)(20,23)(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);(5,6)(7,8)(9,10)(11,20)(12,17)(13,16)(14,24)(15,19)(18,22)(21,23);(2,4)(6,8)(9,11,12,18,22,17,20,10,15,16,23,24,14,21,13,19)

Conjugacy classes & character table

4108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6436);