C₇₉×#11917 #34123606

order	20224
nilpotency class	4
isoclinism	isoclinic class of #11915
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₉×#11917

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₉	#1533
commutator	C₄²	C₂²×C₄×C₇₉
Frattini, cosocle	#97	C₂³×C₇₉
prime radical	#532×C₇₉	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₉ ◁ C₂×C₄×C₇₉ ◁ C₄×M₁₆×C₇₉ ◁ G

280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 2528

A minimal faithful permutation representation — 3 generators on 111 points:

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

Conjugacy classes & character table

2212 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 4905);