Finite Group Databasebeta

← Prev (#49178490) Next (#49178492) →

C3×C5×Dic627 #49178491

order37620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic627
unambiguous semidirect productC3⋊(C3×C5×Dic209)

Splittings

derivedC3×C11×C19 ⋊ C3×C4×C5
HallC32×C5×C11×C19 ⋊ C4
HallC32×C11×C19 ⋊ C4×C5
HallC5×C11×C19 ⋊ C3×Dic3
HallC32×C5×C19 ⋊ Dic11
HallC32×C5×C11 ⋊ Dic19
HallC11×C19 ⋊ C3×C5×Dic3
HallC32×C19 ⋊ C5×Dic11
HallC32×C11 ⋊ C5×Dic19
HallC5×C19 ⋊ C3×Dic33
HallC5×C11 ⋊ C3×Dic57
HallC32×C5 ⋊ Dic209
SylowC19 ⋊ C3×C5×Dic33
SylowC11 ⋊ C3×C5×Dic57
SylowC32 ⋊ C5×Dic209

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D627
commutator, hypocenterC3×C11×C19C3×C4×C5
FrattiniC2C3×C5×D627
Fitting, socle, prime radicalC2×C32×C5×C11×C19C2
cosocleC2×C3×C11×C19C2×C3×C5
LCSG ▷ C3×C11×C19
UCSC1 ◁ C2×C3×C5

112 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12540

Conjugacy classes & character table

9450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 200);