Finite Group Databasebeta

← Prev (#39910460) Next (#39910462) →

D17×D385 #39910461

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

Aliases

direct productD17×D385
unambiguous semidirect product(C5×D17)⋊D77
unambiguous semidirect product(C7×D17)⋊D55
unambiguous semidirect product(C11×D17)⋊D35

Splittings

Fitting, socle, derived, HallC5×C7×C11×C17 ⋊ C22
HallC7×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D11
HallC5×C7×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×D35
HallC7×C17 ⋊ C2×D55
HallC5×C17 ⋊ C2×D77
HallC7×C11 ⋊ D5×D17
HallC5×C11 ⋊ D7×D17
HallC5×C7 ⋊ D11×D17
SylowC17 ⋊ C2×D385
SylowC11 ⋊ D17×D35
SylowC7 ⋊ D17×D55
SylowC5 ⋊ D17×D77

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C11×C17C22
LCSG ▷ C5×C7×C11×C17
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6545

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 83);