Finite Group Databasebeta

← Prev (#20301581) Next (#20301583) →

C3×C5×Dic123 #20301582

order7380
isoclinismisoclinic class of D123
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic123
unambiguous semidirect productC3⋊(C3×C5×Dic41)

Splittings

derivedC3×C41 ⋊ C3×C4×C5
HallC32×C5×C41 ⋊ C4
HallC32×C41 ⋊ C4×C5
HallC5×C41 ⋊ C3×Dic3
HallC32×C5 ⋊ Dic41
SylowC41 ⋊ C3×C5×Dic3
SylowC32 ⋊ C5×Dic41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D123
commutator, hypocenterC3×C41C3×C4×C5
FrattiniC2C3×C5×D123
Fitting, socleC2×C32×C5×C41C2
LCSG ▷ C3×C41
UCSC1 ◁ C2×C3×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1890 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C3⋊(Dic41⋊C25), C3×C25×Dic123, C3×C5×C3⋊(Dic41⋊C5), …
maximal normal subgroup ofC3×C3⋊(Dic41⋊C25), C3×C25×Dic123, C3×C5×C3⋊(Dic41⋊C5), …
maximal quotient ofC3×C25×Dic123, C3×C5×Dic615, C3×C52×Dic123, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 60);