Finite Group Databasebeta

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C5×D17×D77 #39910429

order26180
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D17×D77
unambiguous semidirect product(C7×D17)⋊(C5×D11)

Splittings

Fitting, socle, HallC5×C7×C11×C17 ⋊ C22
derived, HallC7×C11×C17 ⋊ C22×C5
HallC5×C11×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D11
HallC5×C7×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×C5×D7
HallC7×C17 ⋊ C2×C5×D11
HallC5×C17 ⋊ C2×D77
HallC7×C11 ⋊ C2×C5×D17
HallC5×C11 ⋊ D7×D17
HallC5×C7 ⋊ D11×D17
SylowC17 ⋊ C2×C5×D77
SylowC11 ⋊ C5×D7×D17
SylowC7 ⋊ C5×D11×D17

Subgroups

subgroupG/H
center, hypercenterC5D17×D77
commutator, cosocle, hypocenterC7×C11×C17C22×C5
FrattiniC1G
Fitting, socleC5×C7×C11×C17C22
LCSG ▷ C7×C11×C17
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6545

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 51);