C₇₉×#7340 #34119029

order	20224
nilpotency class	5
isoclinism	isoclinic class of #7338
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₇₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₉×#7340

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₉	#1316
commutator	C₂⁴	C₂×C₈×C₇₉
Frattini, cosocle	#407	C₂²×C₇₉
prime radical	C₂³×D₄×C₇₉	C₄
LCS	G ▷ C₂⁴ ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₉ ◁ C₂×C₄×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ #407×C₇₉ ◁ G

452 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 95
transitive degree	μ_t(G) = 1264

A minimal faithful permutation representation — 2 generators on 95 points:

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

Conjugacy classes & character table

2212 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 328);