Finite Group Databasebeta

← Prev (#39910396) Next (#39910398) →

C7×C17×Dic11⋊C5 #39910397

order26180
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C17×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C7×C17)
unambiguous semidirect product(C11⋊C5)⋊(C4×C7×C17)
unambiguous semidirect product(C7×Dic11)⋊(C5×C17)
unambiguous semidirect product(C17×Dic11)⋊(C5×C7)
unambiguous semidirect product(C7×C17×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C4×C5×C7×C17
HallC7×C17×C11⋊C5 ⋊ C4
HallC7×C17×Dic11 ⋊ C5
HallC7×C11×C17 ⋊ C4×C5
HallC17×C11⋊C5 ⋊ C4×C7
HallC17×Dic11 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ C4×C17
HallC7×Dic11 ⋊ C5×C17
HallC11×C17 ⋊ C4×C5×C7
HallC7×C11 ⋊ C4×C5×C17
HallC11⋊C5 ⋊ C4×C7×C17
HallDic11 ⋊ C5×C7×C17

Subgroups

subgroupG/H
center, hypercenterC2×C7×C17AGL(1,𝔽11)
commutator, hypocenterC11C4×C5×C7×C17
FrattiniC2C7×C17×AGL(1,𝔽11)
Fitting, socleC2×C7×C11×C17C2×C5
prime radicalC2×C7×C17×C11⋊C5C2
cosocleC2×C11C2×C5×C7×C17
LCSG ▷ C11
UCSC1 ◁ C2×C7×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5236

Conjugacy classes & character table

2618 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 19);