Dic₉₃₆₇ #49153871

order	37468
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₉₃₆₇
unambiguous semidirect product	C₁₉⋊Dic₄₉₃

Splittings

derived, Hall	C₁₇×C₁₉×C₂₉ ⋊ C₄
Hall	C₁₉×C₂₉ ⋊ Dic₁₇
Hall	C₁₇×C₂₉ ⋊ Dic₁₉
Hall	C₁₇×C₁₉ ⋊ Dic₂₉
Sylow	C₂₉ ⋊ Dic₃₂₃
Sylow	C₁₉ ⋊ Dic₄₉₃
Sylow	C₁₇ ⋊ Dic₅₅₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₉₃₆₇
commutator, hypocenter	C₁₇×C₁₉×C₂₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₇×C₁₉×C₂₉	C₂
LCS	G ▷ C₁₇×C₁₉×C₂₉
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 37468

A minimal faithful permutation representation — 2 generators on 69 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);(1,3,2,4)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)(54,57)(55,56)

Polycyclic presentation:

2,17,19,29,2|a^2=e,b^a=b^16,c^a=c^18,d^a=d^28

Conjugacy classes & character table

9370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37468, 8);

Dic9367 #49153871