Finite Group Databasebeta

← Prev (#14556701) Next (#14556703) →

C5×C9×Dic13 #14556702

order2340
isoclinismisoclinic class of D13
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×Dic13

Splittings

derived, SylowC13 ⋊ C4×C5×C9
HallC5×C9×C13 ⋊ C4
HallC9×C13 ⋊ C4×C5
HallC5×C13 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D13
commutator, hypocenterC13C4×C5×C9
FrattiniC2×C3C3×C5×D13
FittingC2×C5×C9×C13C2
socle, prime radicalC2×C3×C5×C13C2×C3
cosocleC2×C3×C13C2×C3×C5
LCSG ▷ C13
UCSC1 ◁ C2×C5×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 2340

A minimal faithful permutation representation — 2 generators on 31 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);(15,17,16,18)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC9×C25×Dic13, C52×C9×Dic13, C5×C9×Dic65, …
maximal normal subgroup ofC9×C25×Dic13, C52×C9×Dic13, C5×C7×C9×Dic13, …
maximal quotient ofC9×C25×Dic13, C52×C9×Dic13, C5×C9×Dic65, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2340, 6);