C₂×C₇₉×#2030 #34135155

order	20224
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₇₉×#2030

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇₉	#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₇₉
prime radical	C₂⁵×C₇₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂⁵×C₇₉ ◁ G

1482 conjugacy classes of subgroups; only the 350 normal subgroups are shown.

normal subgroups only

This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 350 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) = 105
transitive degree	μ_t(G) = 5056

A minimal faithful permutation representation — 4 generators on 105 points:

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

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, 16454);