C₃⋊#26013829 #45691915

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

Aliases

unambiguous semidirect product

C₃⋊#26013829

Splittings

derived	C₃×C₇²×C₁₉ ⋊ C₃×C₄
Hall	C₃×#14584115 ⋊ C₄
Hall	C₇²×C₁₉ ⋊ C₃×Dic₃
Sylow	C₇² ⋊ Dic₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ C₃⋊#10596873

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊#19150296
commutator, hypocenter	C₃×C₇²×C₁₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×#14584115	C₂
LCS	G ▷ C₃×C₇²×C₁₉
UCS	C₁ ◁ C₂

184 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 41 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) = 1596

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

Polycyclic presentation:

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

Conjugacy classes & character table

1080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 713);