Dic₃₉₉₅ #30630457

order	15980
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₃₉₉₅
unambiguous semidirect product	C₄₇⋊Dic₈₅

Splittings

derived, Hall	C₅×C₁₇×C₄₇ ⋊ C₄
Hall	C₁₇×C₄₇ ⋊ Dic₅
Hall	C₅×C₄₇ ⋊ Dic₁₇
Hall	C₅×C₁₇ ⋊ Dic₄₇
Sylow	C₄₇ ⋊ Dic₈₅
Sylow	C₁₇ ⋊ Dic₂₃₅
Sylow	C₅ ⋊ Dic₇₉₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₉₉₅
commutator, hypocenter	C₅×C₁₇×C₄₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₁₇×C₄₇	C₂
LCS	G ▷ C₅×C₁₇×C₄₇
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 15980

A minimal faithful permutation representation — 2 generators on 73 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);(1,3,2,4)(6,9)(7,8)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(28,73)(29,72)(30,71)(31,70)(32,69)(33,68)(34,67)(35,66)(36,65)(37,64)(38,63)(39,62)(40,61)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)

Polycyclic presentation:

2,5,17,47,2|a^2=e,b^a=b^4,c^a=c^16,d^a=d^46

Conjugacy classes & character table

3998 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₇₉₉₀
maximal normal subgroup of	Dic₇₉₉₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15980, 8);

Dic3995 #30630457