Finite Group Databasebeta

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C5×#21439563 #50303606

order38220
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#21439563

Splittings

derived, HallC13×#3862 ⋊ C4×C5
HallC5×C13×#3862 ⋊ C4
HallC5×C72×C13 ⋊ Dic3
HallC5×#3862 ⋊ Dic13
HallC72×C13 ⋊ C5×Dic3
HallC5×C72 ⋊ Dic39
Hall#3862 ⋊ C5×Dic13
HallC5×C13 ⋊ #10596868
SylowC72 ⋊ C5×Dic39
SylowC13 ⋊ C5×#10596868

Subgroups

subgroupG/H
center, hypercenterC2×C5C13⋊#64418
commutator, hypocenterC13×#3862C4×C5
FrattiniC2C5×C13⋊#64418
Fitting, socleC2×C5×C72×C13D3
prime radicalC2×C5×C13×#3862C2
cosocleC2×C13×#3862C2×C5
LCSG ▷ C13×#3862
UCSC1 ◁ C2×C5

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1820

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 292);