C₃⋊#26013823 #45691909

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₇

Aliases

unambiguous semidirect product

C₃⋊#26013823

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⋊#10596875

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊#19150290
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

136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 38 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)(16,20,19,17,18,21)(23,27,28,24,25,29)(26,35,32,30,31,37)(33,38,40,39,36,34);(1,2,3)(8,9,11,14,13,12,10)(15,16,19,20,18,21,17)(22,23,26,32,38,35,39,25,29,34,40,28,27,33,31,36,37,30,24)

Polycyclic presentation:

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

Conjugacy classes & character table

948 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 707);