C₂²×C₅₉×B(4,𝔽₂) #28472501

order	15104
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅₉ · Schur multiplier (H₂) = C₂¹¹

Aliases

direct product

C₂²×C₅₉×B(4,𝔽₂)

Subgroups

	subgroup	G/H
center, socle	C₂³×C₅₉	#120
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂⁵×C₅₉ ◁ G

7014 conjugacy classes of subgroups; only the 1134 normal subgroups are shown.

normal subgroups only

This group has 7014 conjugacy classes of subgroups — too many to draw. Only its 1134 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) = 71
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 5 generators on 71 points:

(1,2)(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);(3,4);(9,12);(5,6)(7,9)(8,10)(11,12);(5,7)(6,9)(8,11)(10,12)

Conjugacy classes & character table

3776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 53380);