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C11×C19×#4379 #49178653

order37620
automorphism?
homologyAbelianization (H1) = C4×C11×C19 · Schur multiplier (H2) = C3

Aliases

direct productC11×C19×#4379

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C4
derived, HallC32×C5 ⋊ C4×C11×C19
HallC32×C11×C19 ⋊ Dic5
HallC5×C11×C19 ⋊ #157
HallC32×C5×C19 ⋊ C4×C11
HallC32×C5×C11 ⋊ C4×C19
HallC32×C19 ⋊ C11×Dic5
HallC32×C11 ⋊ C19×Dic5
HallC5×C19 ⋊ C11×#157
HallC5×C11 ⋊ C19×#157
SylowC32 ⋊ C11×C19×Dic5
SylowC5 ⋊ C11×C19×#157

Subgroups

subgroupG/H
center, hypercenterC11×C19#4379
commutator, hypocenterC32×C5C4×C11×C19
FrattiniC1G
Fitting, socleC32×C5×C11×C19C4
prime radicalC5×C11×C3⋊D3×C19C2
cosocleC5×C3⋊D3C2×C11×C19
LCSG ▷ C32×C5
UCSC1 ◁ C11×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6270

Conjugacy classes & character table

3762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 362);