C₅₉×#568 #16837102

order	3776
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅₉×#568

Subgroups

	subgroup	G/H
center	C₄×C₅₉	C₂⁴
commutator	C₂	C₂³×C₄×C₅₉
Frattini, cosocle	C₄	C₂⁴×C₅₉
socle	C₂×C₅₉	C₂³×C₄
prime radical	C₂×#41×C₅₉	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₉ ◁ G

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 944

A minimal faithful permutation representation — 4 generators on 75 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₉×#1858, C₅₉×#1861, C₅₉×#1868, …
maximal normal subgroup of	C₅₉×#1858, C₅₉×#1861, C₅₉×#1868, …
maximal quotient of	C₅₉×#2873, C₅₉×#2875, C₅₉×#2879, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 249);

C59×#568 #16837102