C₉×C₂²⋊D₁₉ #13062928

order	1368
isoclinism	isoclinic class of Dic₃₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₉×C₂²⋊D₁₉

Splittings

Fitting	C₂²×C₉×C₁₉ ⋊ C₂
Hall	C₉×C₁₉ ⋊ D₄
Sylow	C₁₉ ⋊ D₄×C₉

Subgroups

	subgroup	G/H
center	C₂×C₉	C₂×D₁₉
commutator	C₂×C₁₉	C₂²×C₉
Frattini	C₂×C₃	C₂×C₃×D₁₉
Fitting	C₂²×C₉×C₁₉	C₂
socle, cosocle	C₂×C₃×C₁₉	C₂²×C₃
prime radical	C₃×C₂²⋊D₁₉	C₃
hypercenter	C₂²×C₉	D₁₉
hypocenter	C₁₉	D₄×C₉
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₉ ◁ C₂²×C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 684

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1368, 28);

C9×C22⋊D19 #13062928