C₁₉⋊C₃×#64418⋊C₂ #45691990

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

Aliases

direct product

C₁₉⋊C₃×#64418⋊C₂

Splittings

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

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 24 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 24 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:

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

Conjugacy classes & character table

171 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 788);