Finite Group Databasebeta

← Prev (#47978384) Next (#47978386) →

C5×C7×Dic23⋊C11 #47978385

order35420
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic23⋊C11
unambiguous semidirect productDic23⋊(C5×C7×C11)
unambiguous semidirect product(C23⋊C11)⋊(C4×C5×C7)
unambiguous semidirect product(C5×Dic23)⋊(C7×C11)
unambiguous semidirect product(C7×Dic23)⋊(C5×C11)
unambiguous semidirect product(C5×C7×Dic23)⋊C11

Splittings

derived, SylowC23 ⋊ C4×C5×C7×C11
HallC5×C7×C23⋊C11 ⋊ C4
HallC5×C7×Dic23 ⋊ C11
HallC7×C23⋊C11 ⋊ C4×C5
HallC5×C23⋊C11 ⋊ C4×C7
HallC5×C7×C23 ⋊ C4×C11
HallC7×Dic23 ⋊ C5×C11
HallC5×Dic23 ⋊ C7×C11
HallC23⋊C11 ⋊ C4×C5×C7
HallC7×C23 ⋊ C4×C5×C11
HallC5×C23 ⋊ C4×C7×C11
HallDic23 ⋊ C5×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7AGL(1,𝔽23)
commutator, hypocenterC23C4×C5×C7×C11
FrattiniC2C5×C7×AGL(1,𝔽23)
Fitting, socleC2×C5×C7×C23C2×C11
prime radicalC2×C5×C7×C23⋊C11C2
cosocleC2×C23C2×C5×C7×C11
LCSG ▷ C23
UCSC1 ◁ C2×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3220

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 19);