Finite Group Databasebeta

← Prev (#24925811) Next (#24925813) →

C5×#10624382⋊C3 #24925812

order10860
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#10624382⋊C3
unambiguous semidirect product(C5×#10624382)⋊C3

Splittings

Fitting, socle, HallC5×C181 ⋊ C3×C4
derived, SylowC181 ⋊ C3×C4×C5
HallC5×#10624382 ⋊ C3
HallC5×C181⋊C3 ⋊ C4
Hall#10624382 ⋊ C3×C5
HallC181⋊C3 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC5#10624382⋊C3
commutator, hypocenterC181C3×C4×C5
FrattiniC1G
Fitting, socleC5×C181C3×C4
prime radicalC5×D181⋊C3C2
cosocleD181C2×C3×C5
LCSG ▷ C181
UCSC1 ◁ C5

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#20266795, C3×C5×#10624382⋊C3, C5×C3⋊(#10624382⋊C3)
maximal normal subgroup ofC5×#20266795, C3×C5×#10624382⋊C3
maximal quotient ofC5×#20266771, C3×C5×#10624382⋊C3, C5×C3⋊(#10624382⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10860, 28);