Finite Group Databasebeta

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C2×C5⋊#16838450 #50304313

order38220
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊#16838450
unambiguous semidirect product(C2×C5)⋊#16838450

Splittings

Fitting, socleC2×C5×C72×C13 ⋊ C2×C3
derived, HallC5×C72×C13 ⋊ C22×C3
HallC2×C5⋊(C7⋊D91) ⋊ C3
HallC5×C13×#3861 ⋊ C22
HallC13×#3861 ⋊ C2×D5
HallC5×#3861 ⋊ C2×D13
HallC72×C13 ⋊ C2×C3×D5
HallC5×C72 ⋊ C2×C3×D13
Hall#3861 ⋊ C2×D65
HallC5×C13 ⋊ C2×#64424
SylowC72 ⋊ C2×C3×D65
SylowC13 ⋊ C2×C5⋊#64424
SylowC5 ⋊ C2×#16838450

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#16838450
commutator, cosocle, hypocenterC5×C72×C13C22×C3
FrattiniC1G
Fitting, socleC2×C5×C72×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1 ◁ C2

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6370

Conjugacy classes & character table

1244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 999);