Finite Group Databasebeta

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C2×C17×D385 #39910495

order26180
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×D385
unambiguous semidirect product(C2×C5)⋊(C17×D77)
unambiguous semidirect product(C2×C7)⋊(C17×D55)
unambiguous semidirect product(C2×C11)⋊(C17×D35)

Splittings

Fitting, socleC2×C5×C7×C11×C17 ⋊ C2
derived, HallC5×C7×C11 ⋊ C22×C17
HallC5×C7×C11×C17 ⋊ C22
HallC7×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D11
HallC11×C17 ⋊ C2×D35
HallC7×C17 ⋊ C2×D55
HallC5×C17 ⋊ C2×D77
HallC7×C11 ⋊ C2×D5×C17
HallC5×C11 ⋊ C2×D7×C17
HallC5×C7 ⋊ C2×C17×D11
SylowC11 ⋊ C2×C17×D35
SylowC7 ⋊ C2×C17×D55
SylowC5 ⋊ C2×C17×D77

Subgroups

subgroupG/H
center, hypercenterC2×C17D385
commutator, cosocle, hypocenterC5×C7×C11C22×C17
FrattiniC1G
Fitting, socleC2×C5×C7×C11×C17C2
LCSG ▷ C5×C7×C11
UCSC1 ◁ C2×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13090

Conjugacy classes & character table

6596 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 117);