C₂×C₇₉×#1658 #34130677

order	20224
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₇₉×#1658

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇₉	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₂×#127×C₇₉	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

882 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 882 conjugacy classes of subgroups — too many to draw. Only its 238 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) = 113
transitive degree	μ_t(G) = 10112

A minimal faithful permutation representation — 4 generators on 113 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);(83,87)(85,92)(88,96)(89,93)(90,94)(95,97)(100,106)(101,108)(103,111)(104,109)(107,110)(112,113);(82,83,86,89)(84,88,91,97)(85,93,92,87)(90,95,94,96)(98,99,102,105)(100,103,107,112)(101,109,108,104)(106,113,110,111);(82,84,86,91)(83,88,89,97)(85,94,92,90)(87,95,93,96)(98,100)(99,103)(101,110)(102,107)(104,113)(105,112)(106,108)(109,111)

Conjugacy classes & character table

3160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 11976);