Dic₁₀₇₃ #16864276

order	4292
automorphism	Aut(G) order 2163168
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic

Dic₁₀₇₃

Splittings

derived, Hall	C₂₉×C₃₇ ⋊ C₄
Sylow	C₃₇ ⋊ Dic₂₉
Sylow	C₂₉ ⋊ Dic₃₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₀₇₃
commutator, hypocenter	C₂₉×C₃₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₂₉×C₃₇	C₂
LCS	G ▷ C₂₉×C₃₇
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 70
transitive degree	μ_t(G) = 4292

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

Polycyclic presentation:

2,29,37,2|a^2=d,b^a=b^28,c^a=c^36

Conjugacy classes & character table

1076 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×Dic₁₀₇₃, Dic₃₂₁₉, Dic₁₀₇₃⋊C₃, …
maximal normal subgroup of	C₃×Dic₁₀₇₃, Dic₁₀₇₃⋊C₃, C₅×Dic₁₀₇₃, …
maximal quotient of	C₃×Dic₁₀₇₃, Dic₃₂₁₉, C₅×Dic₁₀₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4292, 4);

Dic1073 #16864276