C₇₉×#12470 #34124159

order	20224
nilpotency class	4
isoclinism	isoclinic class of #12430
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₇₉×#12470

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₉	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₇₉
prime radical	C₂×D₄×C₇₉	D₈
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₄²×C₇₉ ◁ C₈×D₄×C₇₉ ◁ G

224 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 82 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)(3,5)(4,6)(7,8)(9,10,14,11)(12,21,23,24)(13,20,22,17)(15,16,18,19)(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);(2,5)(6,7)(9,11,18,21,13,20,12,19,14,10,15,24,22,17,23,16);(2,6)(4,8)(5,7)

Conjugacy classes & character table

3871 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 5458);