Finite Group Databasebeta

C13×#15668724 #50303669

order38220
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×#15668724

Splittings

derived, HallC5×#3862 ⋊ C4×C13
HallC5×C13×#3862 ⋊ C4
HallC5×C72×C13 ⋊ Dic3
HallC13×#3862 ⋊ Dic5
HallC72×C13 ⋊ Dic15
HallC5×C72 ⋊ Dic3×C13
Hall#3862 ⋊ C13×Dic5
HallC5×C13 ⋊ #10596868
SylowC72 ⋊ C13×Dic15
SylowC5 ⋊ C13×#10596868

Subgroups

subgroupG/H
center, hypercenterC2×C13C5⋊#64418
commutator, hypocenterC5×#3862C4×C13
FrattiniC2C13×C5⋊#64418
Fitting, socleC2×C5×C72×C13D3
prime radicalC2×C5×C13×#3862C2
cosocleC2×C5×#3862C2×C13
LCSG ▷ C5×#3862
UCSC1 ◁ C2×C13

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1820

Conjugacy classes & character table

1508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 355);