C₂×C₇₉×#1402 #34125248

order	20224
nilpotency class	5
isoclinism	isoclinic class of #1402
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×C₇₉×#1402

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₉	AΣL(1,𝔽₁₆)
commutator	C₂×D₄	C₂²×C₄×C₇₉
Frattini, cosocle	#127	C₂³×C₇₉
prime radical	C₂×#453×C₇₉	C₂
LCS	G ▷ C₂×D₄ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂³×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂×#127×C₇₉ ◁ G

564 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 97
transitive degree	μ_t(G) = 2528

A minimal faithful permutation representation — 3 generators on 97 points:

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

Conjugacy classes & character table

2686 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6547);