Finite Group Databasebeta

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C2×C5×#15667865 #43249686

order28470
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×#15667865

Splittings

Fitting, socle, HallC2×C5×C13×C73 ⋊ C3
derived, HallC13×C73 ⋊ C2×C3×C5
HallC5×C13×C73 ⋊ C2×C3
HallC2×C13×C73 ⋊ C3×C5
HallC2×C5×C73 ⋊ C13⋊C3
HallC5×C73 ⋊ C2×C13⋊C3
HallC2×C73 ⋊ C5×C13⋊C3
HallC2×C5×C13 ⋊ C73⋊C3
SylowC73 ⋊ C2×C5×C13⋊C3
HallC5×C13 ⋊ C2×C73⋊C3
HallC2×C13 ⋊ C5×C73⋊C3
SylowC13 ⋊ C2×C5×C73⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#15667865
commutator, cosocle, hypocenterC13×C73C2×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C13×C73C3
LCSG ▷ C13×C73
UCSC1 ◁ C2×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9490

Conjugacy classes & character table

3190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28470, 5);