Finite Group Databasebeta

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C2×C3×#19149921 #45686772

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

Aliases

direct productC2×C3×#19149921

Splittings

Fitting, socle, HallC2×C3×C11×C101 ⋊ C5
derived, HallC11×C101 ⋊ C2×C3×C5
HallC3×C11×C101 ⋊ C2×C5
HallC2×C11×C101 ⋊ C3×C5
HallC2×C3×C101 ⋊ C11⋊C5
HallC3×C101 ⋊ C2×C11⋊C5
HallC2×C101 ⋊ C3×C11⋊C5
SylowC101 ⋊ C2×C3×C11⋊C5
HallC2×C3×C11 ⋊ C101⋊C5
HallC3×C11 ⋊ C2×C101⋊C5
HallC2×C11 ⋊ C3×C101⋊C5
SylowC11 ⋊ C2×C3×C101⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3#19149921
commutator, cosocle, hypocenterC11×C101C2×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C101C5
LCSG ▷ C11×C101
UCSC1 ◁ C2×C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6666

Conjugacy classes & character table

1362 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33330, 4);