C₂×C₇₉×#1840 #34132460

order	20224
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₇₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₇₉×#1840

Subgroups

	subgroup	G/H
center	C₂³×C₄×C₇₉	C₂³
commutator	C₂³	C₂³×C₄×C₇₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
socle, prime radical	C₂⁴×C₇₉	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₇₉ ◁ G

894 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 462 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) = 20224

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

Conjugacy classes & character table

6952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 13759);