Dic₃₇₄₁ #28418080

order	14964
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₃₇₄₁
unambiguous semidirect product	C₃⋊Dic₁₂₄₇
unambiguous semidirect product	C₄₃⋊Dic₈₇

Splittings

derived, Hall	C₃×C₂₉×C₄₃ ⋊ C₄
Hall	C₂₉×C₄₃ ⋊ Dic₃
Hall	C₃×C₄₃ ⋊ Dic₂₉
Hall	C₃×C₂₉ ⋊ Dic₄₃
Sylow	C₄₃ ⋊ Dic₈₇
Sylow	C₂₉ ⋊ Dic₁₂₉
Sylow	C₃ ⋊ Dic₁₂₄₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₇₄₁
commutator, hypocenter	C₃×C₂₉×C₄₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₂₉×C₄₃	C₂
LCS	G ▷ C₃×C₂₉×C₄₃
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 14964

A minimal faithful permutation representation — 2 generators on 79 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);(1,3,2,4)(6,7)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(38,79)(39,78)(40,77)(41,76)(42,75)(43,74)(44,73)(45,72)(46,71)(47,70)(48,69)(49,68)(50,67)(51,66)(52,65)(53,64)(54,63)(55,62)(56,61)(57,60)(58,59)

Polycyclic presentation:

2,3,29,43,2|a^2=e,b^a=b^2,c^a=c^28,d^a=d^42

Conjugacy classes & character table

3744 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₇₄₈₂
maximal normal subgroup of	Dic₇₄₈₂

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14964, 9);

Dic3741 #28418080