D₁₉⋊C₃×#64418 #45691979

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₁₉⋊C₃×#64418
unambiguous semidirect product	D₁₉⋊(C₃×#64418)

Splittings

Fitting, socle, Hall	C₇²×C₁₉ ⋊ C₂×C₃×D₃
derived	C₁₉×#3862 ⋊ C₂²×C₃
Hall	C₁₉⋊C₃×#3862 ⋊ C₂²
Sylow	C₇² ⋊ D₃×D₁₉⋊C₃
Sylow	C₁₉ ⋊ C₂×C₃×#64418

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₁₉×#3862	C₂²×C₃
Fitting, socle	C₇²×C₁₉	C₂×C₃×D₃
LCS	G ▷ C₁₉×#3862
UCS	C₁

152 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 22 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) = 33
transitive degree	μ_t(G) = 266

A minimal faithful permutation representation — 2 generators on 33 points:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 777);