D₃×#19150296 #45692402

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

Aliases

direct product

D₃×#19150296

Splittings

Fitting, socle, derived	C₃×C₇²×C₁₉ ⋊ C₂²×C₃
Hall	C₃×#14584115 ⋊ C₂²
Hall	C₇²×C₁₉ ⋊ C₂×C₃×D₃
Sylow	C₇² ⋊ C₂×D₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ D₃×#64423

Subgroups

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

230 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 47 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) = 36
transitive degree	μ_t(G) = 798

A minimal faithful permutation representation — 2 generators on 36 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 1200);