D₃×D₁₉⋊#3862 #45692469

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	D₃×D₁₉⋊#3862
unambiguous semidirect product	D₁₉⋊(D₃×#3862)
unambiguous semidirect product	(D₃×D₁₉)⋊#3862

Splittings

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

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

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

normal subgroups only

This group has 216 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) = 1197

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 1267);