C₅₉×#7395 #28419504

order	15104
nilpotency class	5
isoclinism	isoclinic class of #7394
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#7395

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#1343
commutator	C₂×C₂²⋊C₄	C₂×C₄×C₅₉
Frattini, cosocle	#381	C₂²×C₅₉
prime radical	C₅₉×#534	C₄
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂³×C₅₉ ◁ C₂⁴×C₅₉ ◁ C₅₉×#381 ◁ G

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

normal subgroups only

This group has 284 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) = 91
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 2 generators on 91 points:

(1,2,5,9,6,10,18,26)(3,11,13,27,14,23,30,32)(4,15,16,31,17,8,22,24)(7,19,20,12,21,28,25,29)(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);(1,3)(2,7)(4,12)(5,13)(6,14)(8,23)(9,25)(10,21)(11,15)(16,19)(17,29)(18,30)(20,26)(22,28)(24,32)(27,31)

Conjugacy classes & character table

1475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 383);