Finite Group Databasebeta

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C2×C5⋊#16838456 #50304315

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

Aliases

direct productC2×C5⋊#16838456
unambiguous semidirect product(C2×C5)⋊#16838456

Splittings

Fitting, socleC2×C5×C72×C13 ⋊ C2×C3
derived, HallC5×C72×C13 ⋊ C22×C3
HallC2×C7×D455 ⋊ C3
HallC5×#14274263 ⋊ C22
Hall#14274263 ⋊ C2×D5
HallC72×C13 ⋊ C2×C3×D5
HallC5×C72 ⋊ C2×D13⋊C3
HallC5×C13 ⋊ C2×#64423
SylowC72 ⋊ C2×C5⋊(D13⋊C3)
SylowC13 ⋊ C2×C5⋊#64423
SylowC5 ⋊ C2×#16838456

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#16838456
commutator, cosocle, hypocenterC5×C72×C13C22×C3
FrattiniC1G
Fitting, socleC2×C5×C72×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1 ◁ C2

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1820

Conjugacy classes & character table

1090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1001);