Finite Group Databasebeta

← Prev (#19099452) Next (#19099454) →

D55⋊D23 #19099453

order5060
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD55⋊D23
unambiguous semidirect productD115⋊D11
unambiguous semidirect productD253⋊D5

Splittings

Fitting, socle, derived, HallC5×C11×C23 ⋊ C22
HallC11×C23 ⋊ C2×D5
HallC5×C23 ⋊ C2×D11
HallC5×C11 ⋊ C2×D23
SylowC23 ⋊ D5×D11
SylowC11 ⋊ D5×D23
SylowC5 ⋊ D11×D23

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C11×C23C22
LCSG ▷ C5×C11×C23
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,5,11,23|d^a=d^10,e^a=e^22,c^b=c^4,d^b=d^10

Conjugacy classes & character table

347 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D55⋊D23, D253⋊D15, D115⋊D33, …
maximal normal subgroup ofC3×D55⋊D23, D115⋊AGL(1,𝔽11), C5×D55⋊D23, …
maximal quotient ofC3×D55⋊D23, D253⋊D15, D115⋊D33, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5060, 40);