C₆₁×#535 #16839429

order	3904
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₆₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₆₁×#535

Subgroups

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₆₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ G

334 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 162 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) = 73
transitive degree	μ_t(G) = 976

A minimal faithful permutation representation — 4 generators on 73 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)(63,65)(67,70)(68,72);(66,67,69,70)(68,71,72,73);(62,63)(64,65)(66,67)(68,71)(69,70)(72,73);(66,68)(67,71)(69,72)(70,73)

Conjugacy classes & character table

1342 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30598185, #30598536, #30598549, …
maximal subgroup of	C₆₁×#1910, C₆₁×#1911, C₆₁×#1914, …
maximal normal subgroup of	C₆₁×#1910, C₆₁×#1911, C₆₁×#1914, …
maximal quotient of	C₆₁×#2309, C₆₁×#2311, C₆₁×#2317, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 216);