Finite Group Databasebeta

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C2×C3×C5×D559 #46776604

order33540
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D559

Splittings

Fitting, socleC2×C3×C5×C13×C43 ⋊ C2
derived, HallC13×C43 ⋊ C22×C3×C5
HallC3×C5×C13×C43 ⋊ C22
HallC5×C13×C43 ⋊ C22×C3
HallC3×C13×C43 ⋊ C22×C5
HallC3×C5×C43 ⋊ C2×D13
HallC5×C43 ⋊ C2×C3×D13
HallC3×C5×C13 ⋊ C2×D43
HallC3×C43 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×C3×D43
SylowC43 ⋊ C2×C3×C5×D13
HallC3×C13 ⋊ C2×C5×D43
SylowC13 ⋊ C2×C3×C5×D43

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D559
commutator, cosocle, hypocenterC13×C43C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C43C2
LCSG ▷ C13×C43
UCSC1 ◁ C2×C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16770

Conjugacy classes & character table

8430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 224);