C₉×D₇×C₃₁ #16840869

order	3906
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₉×D₇×C₃₁

Splittings

Fitting, Hall	C₇×C₉×C₃₁ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₃₁
Hall	C₇×C₃₁ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₃₁	D₇
commutator, hypocenter	C₇	C₂×C₉×C₃₁
Frattini	C₃	C₃×D₇×C₃₁
Fitting	C₇×C₉×C₃₁	C₂
socle	C₃×C₇×C₃₁	C₂×C₃
prime radical	C₃×D₇×C₃₁	C₃
cosocle	C₃×C₇	C₂×C₃×C₃₁
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₃₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1953

A minimal faithful permutation representation — 2 generators on 47 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(11,16)(12,15)(13,14)

Conjugacy classes & character table

1395 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×D₇×C₃₁, C₉×C₃₁×D₃₅, C₉×D₇×ΓL(1,𝔽₃₂), …
maximal normal subgroup of	C₅×C₉×D₇×C₃₁, C₉×D₇×ΓL(1,𝔽₃₂), C₇×C₉×D₇×C₃₁
maximal quotient of	C₅×C₉×D₇×C₃₁, C₉×C₃₁×D₃₅, C₉×C₃₁×D₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3906, 19);

C9×D7×C31 #16840869