C₁₉×#950 #14269702

order	1824
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#950

Splittings

Fitting	C₃×#41×C₁₉ ⋊ C₂
Hall	C₃×C₁₉ ⋊ #135
Sylow	C₃ ⋊ C₁₉×#135

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#67
commutator, cosocle	C₃×C₄	C₂³×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting	C₃×#41×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂×D₄
hypercenter	#41×C₁₉	D₃
hypocenter	C₃	C₁₉×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₄×C₁₉ ◁ #41×C₁₉

124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 912

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 929);