C₇×C₉×Dic₁₉ #18012102

order	4788
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇×C₉×Dic₁₉

Splittings

derived, Sylow	C₁₉ ⋊ C₄×C₇×C₉
Hall	C₇×C₉×C₁₉ ⋊ C₄
Hall	C₉×C₁₉ ⋊ C₄×C₇
Hall	C₇×C₁₉ ⋊ C₄×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇×C₉	D₁₉
commutator, hypocenter	C₁₉	C₄×C₇×C₉
Frattini	C₂×C₃	C₃×C₇×D₁₉
Fitting	C₂×C₇×C₉×C₁₉	C₂
socle, prime radical	C₂×C₃×C₇×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₁₉	C₂×C₃×C₇
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₇×C₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 4788

A minimal faithful permutation representation — 2 generators on 39 points:

(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16)(17,18)(19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(17,19,18,20)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₇×C₉×Dic₁₉, C₇×C₉×Dic₉₅, C₇×C₉×C₁₉⋊AGL(1,𝔽₅), …
maximal normal subgroup of	C₅×C₇×C₉×Dic₁₉, C₉×C₄₉×Dic₁₉, C₇²×C₉×Dic₁₉
maximal quotient of	C₅×C₇×C₉×Dic₁₉, C₇×C₉×Dic₉₅, C₇×C₉×C₁₉⋊AGL(1,𝔽₅), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 18);

C7×C9×Dic19 #18012102