C₇₉×#13465 #34125154

order	20224
nilpotency class	4
isoclinism	isoclinic class of #13357
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₉×#13465

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₉	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×Q₈	C₂³×C₇₉
prime radical	C₂³×C₇₉	#120
LCS	G ▷ C₂²×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂³×C₇₉ ◁ C₂²×Q₈×C₇₉ ◁ G

384 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 5056

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

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

Conjugacy classes & character table

2449 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6453);