C₃×Dic₉₇ #11923968

order	1164
isoclinism	isoclinic class of D₉₇
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×Dic₉₇

Splittings

derived, Sylow	C₉₇ ⋊ C₃×C₄
Hall	C₃×C₉₇ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₉₇
commutator, hypocenter	C₉₇	C₃×C₄
Frattini	C₂	C₃×D₉₇
Fitting, socle, prime radical	C₂×C₃×C₉₇	C₂
cosocle	C₂×C₉₇	C₂×C₃
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₂×C₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 104
transitive degree	μ_t(G) = 1164

A minimal faithful permutation representation — 2 generators on 104 points:

(1,2,3)(4,5)(6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104);(4,6,5,7)(9,104)(10,103)(11,102)(12,101)(13,100)(14,99)(15,98)(16,97)(17,96)(18,95)(19,94)(20,93)(21,92)(22,91)(23,90)(24,89)(25,88)(26,87)(27,86)(28,85)(29,84)(30,83)(31,82)(32,81)(33,80)(34,79)(35,78)(36,77)(37,76)(38,75)(39,74)(40,73)(41,72)(42,71)(43,70)(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(56,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	Dic₉₇⋊C₉, C₉×Dic₉₇, C₃×Dic₉₇⋊C₃, …
maximal normal subgroup of	Dic₉₇⋊C₉, C₉×Dic₉₇, C₃×Dic₉₇⋊C₃, …
maximal quotient of	C₉×Dic₉₇, C₃²×Dic₉₇, C₃×Dic₂₉₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1164, 4);

C3×Dic97 #11923968