Dic₇₇₃₃ #44525816

order	30932
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₇₇₃₃
unambiguous semidirect product	C₁₁⋊Dic₇₀₃
unambiguous semidirect product	C₁₉⋊Dic₄₀₇

Splittings

derived, Hall	C₁₁×C₁₉×C₃₇ ⋊ C₄
Hall	C₁₉×C₃₇ ⋊ Dic₁₁
Hall	C₁₁×C₃₇ ⋊ Dic₁₉
Hall	C₁₁×C₁₉ ⋊ Dic₃₇
Sylow	C₃₇ ⋊ Dic₂₀₉
Sylow	C₁₉ ⋊ Dic₄₀₇
Sylow	C₁₁ ⋊ Dic₇₀₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₇₃₃
commutator, hypocenter	C₁₁×C₁₉×C₃₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₁₉×C₃₇	C₂
LCS	G ▷ C₁₁×C₁₉×C₃₇
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 30932

A minimal faithful permutation representation — 2 generators on 71 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(36,71)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,64)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58)(50,57)(51,56)(52,55)(53,54)

Polycyclic presentation:

2,11,19,37,2|a^2=e,b^a=b^10,c^a=c^18,d^a=d^36

Conjugacy classes & character table

7736 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₅₄₆₆
maximal normal subgroup of	Dic₁₅₄₆₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30932, 8);

Dic7733 #44525816