C₃⋊#26013834 #45691920

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product

C₃⋊#26013834

Splittings

derived	C₃×C₇²×C₁₉ ⋊ C₃×C₄
Hall	C₃×C₁₉⋊#3862 ⋊ C₄
Hall	C₇²×C₁₉ ⋊ C₃×Dic₃
Sylow	C₇² ⋊ C₃⋊((C₁₉⋊C₃)⋊C₄)
Sylow	C₁₉ ⋊ C₃⋊#10596872

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊#19150301
commutator, hypocenter	C₃×C₇²×C₁₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉⋊#3862	C₂
LCS	G ▷ C₃×C₇²×C₁₉
UCS	C₁ ◁ C₂

120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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) = 40
transitive degree	μ_t(G) = 4788

A minimal faithful permutation representation — 2 generators on 40 points:

(2,3)(4,5,6,7)(9,12,13,10,11,14)(16,17,18)(19,21,20)(23,27,28,24,25,29)(26,34,35,30,31,39)(32,40,38,37,36,33);(1,2,3)(8,9,11,14,13,12,10)(15,16,18,20,17,19,21)(22,23,26,31,36,39,38,28,27,32,37,25,29,33,35,40,34,30,24)

Polycyclic presentation:

2,3^2,7^2,19,2|a^2=g,c^a=c^2,d^a=d^6,f^a=f^18,d^b=d^2,e^b=e^4,f^b=f^11

Conjugacy classes & character table

954 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 718);