Finite Group Databasebeta

← Prev (#19099426) Next (#19099428) →

C11⋊C5×Dic23 #19099427

order5060
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×Dic23
unambiguous semidirect productC23⋊(C4×C11⋊C5)
unambiguous semidirect product(C11×Dic23)⋊C5

Splittings

derived, HallC11×C23 ⋊ C4×C5
HallC23×C11⋊C5 ⋊ C4
HallC11×Dic23 ⋊ C5
SylowC23 ⋊ C4×C11⋊C5
SylowC11 ⋊ C5×Dic23

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D23×C11⋊C5
commutator, hypocenterC11×C23C4×C5
Fitting, socleC2×C11×C23C2×C5
LCSG ▷ C11×C23
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊C5×Dic23, C11⋊C5×Dic69, C5×C11⋊C5×Dic23, …
maximal normal subgroup ofC3×C11⋊C5×Dic23, C5×C11⋊C5×Dic23, C7×C11⋊C5×Dic23
maximal quotient ofC3×C11⋊C5×Dic23, C11⋊C5×Dic69, Dic23×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5060, 14);