C₇₉×#7481 #34119170

order	20224
nilpotency class	5
isoclinism	isoclinic class of #7481
automorphism	?
homology	Abelianization (H₁) = C₄²×C₇₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₉×#7481

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₉	#1390
commutator	C₂×Q₈	C₄²×C₇₉
Frattini, cosocle	C₂×#124	C₂²×C₇₉
prime radical	C₂²×D₄×C₇₉	D₄
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₉ ◁ C₂³×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂×#124×C₇₉ ◁ G

284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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 — 2 generators on 111 points:

(1,2)(3,11,13,27)(4,16,17,26)(5,19,21,10)(6,9)(7,12,22,30)(8,18)(14,29,15,28)(20,25)(23,31,24,32)(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)(2,7,9,23)(4,12)(5,13)(6,15)(8,11,25,28)(10,22,19,24)(14,21)(16,27,26,29)(17,31)(18,32)(20,30)

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, 469);