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C3×#26013191 #45686794

order33330
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×#26013191

Splittings

Fitting, socle, HallC3×C11×C101 ⋊ C2×C5
derived, HallC11×C101 ⋊ C2×C3×C5
HallC3×#19149922 ⋊ C2
HallC3×C11×D101 ⋊ C5
Hall#19149922 ⋊ C2×C3
HallC11×D101 ⋊ C3×C5
HallC3×D101 ⋊ C11⋊C5
HallC3×C101 ⋊ C2×C11⋊C5
HallD101 ⋊ C3×C11⋊C5
SylowC101 ⋊ C2×C3×C11⋊C5
HallC3×C11 ⋊ D101⋊C5
SylowC11 ⋊ C3×D101⋊C5

Subgroups

subgroupG/H
center, hypercenterC3#26013191
commutator, cosocle, hypocenterC11×C101C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C101C2×C5
LCSG ▷ C11×C101
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3333

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33330, 26);