C₁₃×D₇×C₇₃ #27210784

order	13286
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₇×C₇₃
unambiguous semidirect product	C₇⋊(C₂×C₁₃×C₇₃)

Splittings

Fitting, socle, Hall	C₇×C₁₃×C₇₃ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₁₃×C₇₃
Hall	C₇×C₇₃ ⋊ C₂×C₁₃
Hall	C₇×C₁₃ ⋊ C₂×C₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃×C₇₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₁₃×C₇₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₇₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₃×C₇₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 93
transitive degree	μ_t(G) = 6643

A minimal faithful permutation representation — 2 generators on 93 points:

(2,3)(4,5)(6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93);(1,2,4,6,7,5,3)

Conjugacy classes & character table

4745 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₃×D₇×D₇₃, D₇×D₁₃×C₇₃, D₇×D₉₄₉, …
maximal normal subgroup of	C₁₃×D₇×D₇₃, D₇×D₁₃×C₇₃, D₇×D₉₄₉, …
maximal quotient of	C₁₃×Dic₇×C₇₃, C₂×C₁₃×D₇×C₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13286, 5);

C13×D7×C73 #27210784