C₅₉×#12774 #28424883

order	15104
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅₉×#12774

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	B(4,𝔽₂)
commutator	C₂×Q₈	C₂²×C₄×C₅₉
Frattini, cosocle	C₂²×Q₈	C₂³×C₅₉
prime radical	C₂×C₅₉×H(3,𝔽₄)	C₂
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂³×C₅₉ ◁ C₂²×Q₈×C₅₉ ◁ G

932 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 79
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 3 generators on 79 points:

(1,2)(3,4)(5,6,9,12,10,15,8,14)(7,11,18,19,16,13,17,20)(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);(6,11)(7,16)(8,9)(12,19)(13,15)(14,20);(2,4)(6,12)(8,9)(11,19)(13,20)(14,15)(17,18)

Conjugacy classes & character table

2006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5762);