Finite Group Databasebeta

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C5×C13⋊#64418 #34062111

order19110
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13⋊#64418
unambiguous semidirect productC13⋊(C5×#64418)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ D3
derived, HallC13×#3862 ⋊ C2×C5
HallC5×C13×#3862 ⋊ C2
HallC5×#3862 ⋊ D13
HallC72×C13 ⋊ C5×D3
HallC5×C72 ⋊ D39
Hall#3862 ⋊ C5×D13
HallC5×C13 ⋊ #64418
SylowC72 ⋊ C5×D39
SylowC13 ⋊ C5×#64418

Subgroups

subgroupG/H
center, hypercenterC5C13⋊#64418
commutator, cosocle, hypocenterC13×#3862C2×C5
FrattiniC1G
Fitting, socleC5×C72×C13D3
LCSG ▷ C13×#3862
UCSC1 ◁ C5

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 910

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D13×#64418, C5×#64418⋊D13, C5×#21439671, …
maximal normal subgroup ofC5×D13×#64418, C5×#64418⋊D13, C5×#21439671, …
maximal quotient ofC5×#21439563, C2×C5×C13⋊#64418

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 104);