C₅₉×#349 #16836883

order	3776
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#349

Subgroups

	subgroup	G/H
center	C₄×C₅₉	C₂²⋊C₄
commutator	C₂²	C₂×C₈×C₅₉
Frattini, cosocle	C₂×C₈	C₂²×C₅₉
socle	C₂×C₅₉	C₂²⋊C₈
prime radical	C₂³×C₅₉	C₈
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₉ ◁ C₂×C₈×C₅₉ ◁ G

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 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)(60,61,62,66,63,67,69,73,64,65,68,71,70,72,74,75);(61,65)(62,68)(67,72)(69,74)

Conjugacy classes & character table

1298 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅₉×#1320, C₅₉×#1321, C₅₉×#1327, …
maximal normal subgroup of	C₅₉×#1320, C₅₉×#1321, C₅₉×#1327, …
maximal quotient of	C₅₉×#1314, C₅₉×#1322, C₅₉×#1330, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 30);

C59×#349 #16836883