Finite Group Databasebeta

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Cayley diagram

Dic95 #67411

order380
isoclinismisoclinic class of D95
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic95
unambiguous semidirect productC19⋊Dic5

Splittings

derived, HallC5×C19 ⋊ C4
SylowC19 ⋊ Dic5
SylowC5 ⋊ Dic19

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D95
commutator, hypocenterC5×C19C4
Fitting, socle, prime radical, cosocleC2×C5×C19C2
LCSG ▷ C5×C19
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 380

A minimal faithful permutation representation — 2 generators on 28 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);(1,3,2,4)(6,9)(7,8)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)

Polycyclic presentation:

2^2,5,19|a^2=b,c^a=c^4,d^a=d^18

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×D19, D5×Dic19, #10625573, …
maximal normal subgroup ofDic5×D19, D5×Dic19, #10625573, …
maximal quotient ofC19⋊#168, C2×Dic95, C3×Dic95, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(380, 3);