C₂×D₃×#14584115 #45692636

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

Aliases

direct product	C₂×D₃×#14584115
unambiguous semidirect product	C₃⋊(C₂²×#14584115)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×#14584115)

Splittings

Fitting, socle	C₂×C₃×C₇²×C₁₉ ⋊ C₂×C₃
derived	C₃×C₇²×C₁₉ ⋊ C₂²×C₃
Hall	C₃×#14584115 ⋊ C₂²
Hall	C₇²×C₁₉ ⋊ C₂×C₃×D₃
Sylow	C₇² ⋊ C₂×D₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ C₂×D₃×#3861

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₃×#14584115
commutator, cosocle, hypocenter	C₃×C₇²×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇²×C₁₉
UCS	C₁ ◁ C₂

440 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 147 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) = 38
transitive degree	μ_t(G) = 5586

A minimal faithful permutation representation — 3 generators on 38 points:

(4,5)(7,8,9)(10,12,11)(14,15,16)(17,19,18)(21,22,24)(23,26,27)(25,29,28)(30,34,32)(31,35,33)(36,38,37);(1,2)(3,4,5)(13,14,15,17,16,18,19)(20,21,23,27,32,37,34,22,25,30,35,24,28,33,26,31,36,38,29);(6,7,8,10,9,11,12)

Conjugacy classes & character table

1878 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 1434);