Finite Group Databasebeta

← Prev (#44525437) Next (#44525439) →

C5×Dic5×C103⋊C3 #44525438

order30900
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic5×C103⋊C3
unambiguous semidirect product(Dic5×C103)⋊(C3×C5)
unambiguous semidirect product(C5×Dic5×C103)⋊C3

Splittings

derivedC5×C103 ⋊ C3×C4×C5
HallC5×Dic5×C103 ⋊ C3
HallC52×C103⋊C3 ⋊ C4
HallC52×C103 ⋊ C3×C4
SylowC103 ⋊ C3×C5×Dic5
SylowC52 ⋊ C4×C103⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5D5×C103⋊C3
commutator, hypocenterC5×C103C3×C4×C5
FrattiniC2C5×D5×C103⋊C3
Fitting, socleC2×C52×C103C2×C3
prime radicalC2×C52×C103⋊C3C2
cosocleC2×C5×C103C2×C3×C5
LCSG ▷ C5×C103
UCSC1 ◁ C2×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2060

Conjugacy classes & character table

1480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30900, 44);