C₇×C₃₁⋊C₉ #14519868

order	1953
isoclinism	isoclinic class of C₃₁⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₃₁⋊C₉
unambiguous semidirect product	C₃₁⋊(C₇×C₉)

Splittings

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

Subgroups

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×D₃₁⋊C₉, D₇×C₃₁⋊C₉, (C₃₁⋊C₉)⋊D₇, …
maximal normal subgroup of	C₇×D₃₁⋊C₉, D₇×C₃₁⋊C₉, (C₃₁⋊C₉)⋊D₇, …
maximal quotient of	C₂×C₇×C₃₁⋊C₉, C₄₉×C₃₁⋊C₉, C₇²×C₃₁⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1953, 2);

C7×C31⋊C9 #14519868