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C13×C43×Dic15 #46776397

order33540
automorphism?
homologyAbelianization (H1) = C4×C13×C43 · Schur multiplier (H2) = C1

Aliases

direct productC13×C43×Dic15
unambiguous semidirect productC3⋊(C13×Dic5×C43)

Splittings

derived, HallC3×C5 ⋊ C4×C13×C43
HallC3×C5×C13×C43 ⋊ C4
HallC5×C13×C43 ⋊ Dic3
HallC3×C13×C43 ⋊ Dic5
HallC3×C5×C43 ⋊ C4×C13
HallC5×C43 ⋊ Dic3×C13
HallC3×C5×C13 ⋊ C4×C43
HallC3×C43 ⋊ C13×Dic5
HallC5×C13 ⋊ Dic3×C43
HallC3×C13 ⋊ Dic5×C43
SylowC5 ⋊ Dic3×C13×C43
SylowC3 ⋊ C13×Dic5×C43

Subgroups

subgroupG/H
center, hypercenterC2×C13×C43D15
commutator, hypocenterC3×C5C4×C13×C43
FrattiniC2C13×D15×C43
Fitting, socle, prime radicalC2×C3×C5×C13×C43C2
cosocleC2×C3×C5C2×C13×C43
LCSG ▷ C3×C5
UCSC1 ◁ C2×C13×C43

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33540

Conjugacy classes & character table

10062 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 17);