D₉×C₆₇ #11925852

order	1206
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₉×C₆₇
unambiguous semidirect product	C₉⋊(C₂×C₆₇)

Splittings

Fitting, Hall	C₉×C₆₇ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₆₇	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₆₇
Frattini	C₃	D₃×C₆₇
Fitting	C₉×C₆₇	C₂
socle	C₃×C₆₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₆₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 76
transitive degree	μ_t(G) = 603

A minimal faithful permutation representation — 2 generators on 76 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₉×D₆₇, C₂×D₉×C₆₇, C₁₁×D₉×C₆₇, …
maximal normal subgroup of	D₉×D₆₇, C₂×D₉×C₆₇, C₁₁×D₉×C₆₇, …
maximal quotient of	Dic₉×C₆₇, C₂×D₉×C₆₇, C₁₁×D₉×C₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1206, 3);

D9×C67 #11925852