C₆₇×D₉₉ #27210696

order	13266
isoclinism	isoclinic class of D₉₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₇×D₉₉
unambiguous semidirect product	C₉⋊(D₁₁×C₆₇)
unambiguous semidirect product	C₁₁⋊(D₉×C₆₇)

Splittings

Fitting, Hall	C₉×C₁₁×C₆₇ ⋊ C₂
derived, Hall	C₉×C₁₁ ⋊ C₂×C₆₇
Hall	C₁₁×C₆₇ ⋊ D₉
Hall	C₉×C₆₇ ⋊ D₁₁
Sylow	C₁₁ ⋊ D₉×C₆₇
Sylow	C₉ ⋊ D₁₁×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₆₇	D₉₉
commutator, cosocle, hypocenter	C₉×C₁₁	C₂×C₆₇
Frattini	C₃	D₃₃×C₆₇
Fitting	C₉×C₁₁×C₆₇	C₂
socle	C₃×C₁₁×C₆₇	D₃
LCS	G ▷ C₉×C₁₁
UCS	C₁ ◁ C₆₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 6633

A minimal faithful permutation representation — 2 generators on 87 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,15)(14,18)(16,17)(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);(1,2,4,6,8,10,11,9,7,5,3)(12,20,15,18,17,16,14,13,19)

Conjugacy classes & character table

3417 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₆₇×D₉₉, D₉×D₁₁×C₆₇, D₉₉⋊D₆₇, …
maximal normal subgroup of	D₆₇×D₉₉, D₉×D₁₁×C₆₇, D₉₉⋊D₆₇, …
maximal quotient of	C₆₇×Dic₉₉, C₂×C₆₇×D₉₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 10);

C67×D99 #27210696