C₃²×D₈₉ #13107935

order	1602
isoclinism	isoclinic class of D₈₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×D₈₉
unambiguous semidirect product	C₈₉⋊(C₂×C₃²)

Splittings

Fitting, socle, Hall	C₃²×C₈₉ ⋊ C₂
derived, Sylow	C₈₉ ⋊ C₂×C₃²

Subgroups

	subgroup	G/H
center, hypercenter	C₃²	D₈₉
commutator, cosocle, hypocenter	C₈₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₈₉	C₂
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₃²

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 801

A minimal faithful permutation representation — 2 generators on 95 points:

(1,2,3)(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(4,5,6)(8,95)(9,94)(10,93)(11,92)(12,91)(13,90)(14,89)(15,88)(16,87)(17,86)(18,85)(19,84)(20,83)(21,82)(22,81)(23,80)(24,79)(25,78)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃²×#67063, C₃×C₃⋊#67063, C₃×D₃×D₈₉, …
maximal normal subgroup of	C₃²×#67063, C₃×C₃⋊#67063, C₃×D₃×D₈₉, …
maximal quotient of	C₃²×Dic₈₉, C₂×C₃²×D₈₉, C₃×ΓL(1,𝔽₈)⋊D₈₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1602, 5);

C32×D89 #13107935