C₇₉×#7432 #34119121

order	20224
nilpotency class	5
isoclinism	isoclinic class of #7396
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₇₉×#7432

Subgroups

	subgroup	G/H
center	C₄×C₇₉	#353
commutator	C₂×M₁₆	C₂×C₄×C₇₉
Frattini, cosocle	#407	C₂²×C₇₉
socle	C₂×C₇₉	#1352
prime radical	C₂⁴×C₇₉	SD₁₆
LCS	G ▷ C₂×M₁₆ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₉ ◁ C₂×C₄×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ #407×C₇₉ ◁ G

210 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 42 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) = 95
transitive degree	μ_t(G) = 1264

A minimal faithful permutation representation — 2 generators on 95 points:

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

Conjugacy classes & character table

2449 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 420);