Finite Group Databasebeta

← Prev (#39910395) Next (#39910397) →

C7×C11⋊C5×Dic17 #39910396

order26180
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11⋊C5×Dic17
unambiguous semidirect product(C11×Dic17)⋊(C5×C7)
unambiguous semidirect product(C7×C11×Dic17)⋊C5

Splittings

derived, HallC11×C17 ⋊ C4×C5×C7
HallC7×C17×C11⋊C5 ⋊ C4
HallC7×C11×Dic17 ⋊ C5
HallC7×C11×C17 ⋊ C4×C5
HallC17×C11⋊C5 ⋊ C4×C7
HallC11×Dic17 ⋊ C5×C7
HallC7×C17 ⋊ C4×C11⋊C5
HallC7×C11 ⋊ C5×Dic17
SylowC17 ⋊ C4×C7×C11⋊C5
SylowC11 ⋊ C5×C7×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C7D17×C11⋊C5
commutator, hypocenterC11×C17C4×C5×C7
FrattiniC2C7×D17×C11⋊C5
Fitting, socleC2×C7×C11×C17C2×C5
prime radicalC2×C7×C17×C11⋊C5C2
cosocleC2×C11×C17C2×C5×C7
LCSG ▷ C11×C17
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5236

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 18);