C₇₉×#18552 #34130241

order	20224
nilpotency class	3
isoclinism	isoclinic class of #18524
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₇₉×#18552

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₂×#555×C₇₉	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

982 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 230 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) = 111
transitive degree	μ_t(G) = 5056

A minimal faithful permutation representation — 4 generators on 111 points:

(1,2)(3,10)(4,7)(5,8)(6,12)(9,14)(11,15)(13,16)(17,18,22,25)(19,27,30,31)(20,26,21,24)(23,29,32,28)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(1,3,5,13)(2,6,8,15)(4,11,14,12)(7,10,9,16)(17,19,22,30)(18,23,25,32)(20,29,21,28)(24,31,26,27);(1,4,5,14)(2,7,8,9)(3,11,13,12)(6,10,15,16)(18,24)(20,21)(23,31)(25,26)(27,32)(28,29);(2,8)(6,15)(7,9)(10,16)(18,25)(23,32)(24,26)(27,31)

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, 11540);