Finite Group Databasebeta

← Prev (#26044036) Next (#26044038) →

C5×D1173 #26044037

order11730
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1173
unambiguous semidirect productC3⋊(C5×D391)
unambiguous semidirect productC17⋊(C5×D69)
unambiguous semidirect productC23⋊(C5×D51)

Splittings

Fitting, socle, HallC3×C5×C17×C23 ⋊ C2
derived, HallC3×C17×C23 ⋊ C2×C5
HallC5×C17×C23 ⋊ D3
HallC17×C23 ⋊ C5×D3
HallC3×C5×C23 ⋊ D17
HallC3×C5×C17 ⋊ D23
HallC5×C23 ⋊ D51
HallC5×C17 ⋊ D69
HallC3×C23 ⋊ C5×D17
HallC3×C17 ⋊ C5×D23
SylowC23 ⋊ C5×D51
SylowC17 ⋊ C5×D69
HallC3×C5 ⋊ D391
SylowC3 ⋊ C5×D391

Subgroups

subgroupG/H
center, hypercenterC5D1173
commutator, cosocle, hypocenterC3×C17×C23C2×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C23C2
LCSG ▷ C3×C17×C23
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D23×D51, C5×D17×D69, C5×D3×D391, …
maximal normal subgroup ofC5×D23×D51, C5×D17×D69, C5×D3×D391, …
maximal quotient ofC5×Dic1173, C2×C5×D1173, C5×D3519, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11730, 12);