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C17×C31×Dic15 #44539259

order31620
automorphism?
homologyAbelianization (H1) = C4×C17×C31 · Schur multiplier (H2) = C1

Aliases

direct productC17×C31×Dic15
unambiguous semidirect productC3⋊(C17×Dic5×C31)

Splittings

derived, HallC3×C5 ⋊ C4×C17×C31
HallC3×C5×C17×C31 ⋊ C4
HallC5×C17×C31 ⋊ Dic3
HallC3×C17×C31 ⋊ Dic5
HallC3×C5×C31 ⋊ C4×C17
HallC3×C5×C17 ⋊ C4×C31
HallC5×C31 ⋊ Dic3×C17
HallC3×C31 ⋊ C17×Dic5
HallC5×C17 ⋊ Dic3×C31
HallC3×C17 ⋊ Dic5×C31
SylowC5 ⋊ Dic3×C17×C31
SylowC3 ⋊ C17×Dic5×C31

Subgroups

subgroupG/H
center, hypercenterC2×C17×C31D15
commutator, hypocenterC3×C5C4×C17×C31
FrattiniC2C17×D15×C31
Fitting, socle, prime radicalC2×C3×C5×C17×C31C2
cosocleC2×C3×C5C2×C17×C31
LCSG ▷ C3×C5
UCSC1 ◁ C2×C17×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31620

Conjugacy classes & character table

9486 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 16);