Finite Group Databasebeta

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C2×C72×C13×D15 #50304527

order38220
automorphism?
homologyAbelianization (H1) = C22×C72×C13 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C72×C13×D15
unambiguous semidirect product(C2×C3)⋊(C72×D5×C13)
unambiguous semidirect product(C2×C5)⋊(D3×C72×C13)

Splittings

Fitting, socleC2×C3×C5×C72×C13 ⋊ C2
derived, HallC3×C5 ⋊ C22×C72×C13
HallC3×C5×C72×C13 ⋊ C22
HallC5×C72×C13 ⋊ C2×D3
HallC3×C72×C13 ⋊ C2×D5
HallC3×C5×C72 ⋊ C22×C13
HallC5×C72 ⋊ C2×D3×C13
HallC3×C5×C13 ⋊ C22×C72
HallC3×C72 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×D3×C72
HallC3×C13 ⋊ C2×C72×D5
SylowC5 ⋊ C2×D3×C72×C13
SylowC3 ⋊ C2×C72×D5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C72×C13D15
commutator, cosocle, hypocenterC3×C5C22×C72×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C13C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C72×C13

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19110

Conjugacy classes & character table

11466 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1213);