Finite Group Databasebeta

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C5×C13⋊C3×Dic43 #46776402

order33540
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13⋊C3×Dic43

Splittings

derived, HallC13×C43 ⋊ C3×C4×C5
HallC5×C13×Dic43 ⋊ C3
HallC5×C13⋊C3×C43 ⋊ C4
HallC5×C13×C43 ⋊ C3×C4
HallC13×Dic43 ⋊ C3×C5
HallC13⋊C3×C43 ⋊ C4×C5
HallC5×C43 ⋊ C4×C13⋊C3
HallC5×C13 ⋊ C3×Dic43
SylowC43 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C3×C5×Dic43

Subgroups

subgroupG/H
center, hypercenterC2×C5C13⋊C3×D43
commutator, hypocenterC13×C43C3×C4×C5
FrattiniC2C5×C13⋊C3×D43
Fitting, socleC2×C5×C13×C43C2×C3
prime radicalC2×C5×C13⋊C3×C43C2
cosocleC2×C13×C43C2×C3×C5
LCSG ▷ C13×C43
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11180

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 22);