C₂×AGL(1,ℤ/8)×C₇₁ #17985704

order	4544
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×AGL(1,ℤ/8)×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂⁴×C₇₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂²×C₄×C₇₁ ◁ G

298 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 162 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) = 81
transitive degree	μ_t(G) = 1136

A minimal faithful permutation representation — 4 generators on 81 points:

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

Conjugacy classes & character table

1562 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×#1883, C₇₁×#1903, C₇₁×#1904, …
maximal normal subgroup of	C₇₁×#1883, C₇₁×#1903, C₇₁×#1904, …
maximal quotient of	C₂×#418×C₇₁, C₂×#417×C₇₁, C₂×#428×C₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 254);