C₇₉×#11559 #34123248

order	20224
nilpotency class	4
isoclinism	isoclinic class of #11541
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₇₉×#11559

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₇₉
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₇₉
prime radical	C₂×#120×C₇₉	C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂×C₄×D₄×C₇₉ ◁ G

532 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 2528

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

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

Conjugacy classes & character table

2923 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 4547);