Finite Group Databasebeta

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C2×C5⋊((C13⋊C9)⋊D7) #30655102

order16380
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊((C13⋊C9)⋊D7)
unambiguous semidirect product(C2×C5)⋊((C13⋊C9)⋊D7)
unambiguous semidirect product(C2×C13⋊C9)⋊D35

Splittings

derived, HallC5×C7×C13 ⋊ C22×C9
HallC5×C7×C13⋊C9 ⋊ C22
HallC2×D455 ⋊ C9
HallC7×C13⋊C9 ⋊ C2×D5
HallC5×C13⋊C9 ⋊ C2×D7
HallC13⋊C9 ⋊ C2×D35
HallC7×C13 ⋊ C2×C9×D5
HallC5×C13 ⋊ C2×C9×D7
HallC5×C7 ⋊ C2×D13⋊C9
SylowC13 ⋊ C2×C9×D35
SylowC7 ⋊ C2×C5⋊(D13⋊C9)
SylowC5 ⋊ C2×(C13⋊C9)⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊((C13⋊C3)⋊D7)
commutator, hypocenterC5×C7×C13C22×C9
FrattiniC3C2×C5⋊((C13⋊C3)⋊D7)
Fitting, socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×D455C3
cosocleC3×C5×C7×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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) = 8190

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 152);