D₁₉⋊C₃×#64424 #45692069

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product

D₁₉⋊C₃×#64424

Splittings

Fitting, socle, derived, Hall	C₇²×C₁₉ ⋊ C₂²×C₃²
Hall	C₁₉⋊C₃×#3861 ⋊ C₂²
Hall	D₁₉×C₇⋊D₇ ⋊ C₃²
Sylow	C₇² ⋊ C₂×C₃×D₁₉⋊C₃
Sylow	C₁₉ ⋊ C₂×C₃×#64424

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₁₉	C₂²×C₃²
LCS	G ▷ C₇²×C₁₉
UCS	C₁

600 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 79 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) = 931

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 867);