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C₉×C₁₉×Dic₇ #18012103

order	4788
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₉×Dic₇

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	D₇
commutator, hypocenter	C₇	C₄×C₉×C₁₉
Frattini	C₂×C₃	C₃×D₇×C₁₉
Fitting	C₂×C₇×C₉×C₁₉	C₂
socle, prime radical	C₂×C₃×C₇×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₇	C₂×C₃×C₁₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₉×C₁₉

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);(29,31,30,32)(34,39)(35,38)(36,37)

Conjugacy classes & character table

1710 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×C₁₉×Dic₇, C₉×C₁₉×Dic₃₅, C₉×C₁₉×C₇⋊AGL(1,𝔽₅), …
maximal normal subgroup of	C₅×C₉×C₁₉×Dic₇, C₇×C₉×C₁₉×Dic₇
maximal quotient of	C₅×C₉×C₁₉×Dic₇, C₉×C₁₉×Dic₃₅, C₉×C₁₉×C₇⋊AGL(1,𝔽₅), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 19);