C₄₇×#10624563 #46804204

order	34263
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₃³×C₄₇ · Schur multiplier (H₂) = C₃⁵

Aliases

direct product

C₄₇×#10624563

Subgroups

	subgroup	G/H
center, socle	C₃³×C₄₇	C₃³
commutator, Frattini, cosocle	C₃³	C₃³×C₄₇
prime radical	C₃²×H(3,𝔽₃)×C₄₇	C₃
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃³×C₄₇ ◁ G

758 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 152 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) = 74
transitive degree	μ_t(G) = 11421

A minimal faithful permutation representation — 3 generators on 74 points:

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

Conjugacy classes & character table

4935 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34263, 123);