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C31×Dic255 #44539261

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

Aliases

direct productC31×Dic255
unambiguous semidirect productC3⋊(C31×Dic85)

Splittings

derived, HallC3×C5×C17 ⋊ C4×C31
HallC3×C5×C17×C31 ⋊ C4
HallC5×C17×C31 ⋊ Dic3
HallC3×C17×C31 ⋊ Dic5
HallC17×C31 ⋊ Dic15
HallC3×C5×C31 ⋊ Dic17
HallC5×C31 ⋊ Dic51
HallC3×C31 ⋊ Dic85
HallC5×C17 ⋊ Dic3×C31
HallC3×C17 ⋊ Dic5×C31
SylowC17 ⋊ C31×Dic15
HallC3×C5 ⋊ C31×Dic17
SylowC5 ⋊ C31×Dic51
SylowC3 ⋊ C31×Dic85

Subgroups

subgroupG/H
center, hypercenterC2×C31D255
commutator, hypocenterC3×C5×C17C4×C31
FrattiniC2C31×D255
Fitting, socle, prime radicalC2×C3×C5×C17×C31C2
cosocleC2×C3×C5×C17C2×C31
LCSG ▷ C3×C5×C17
UCSC1 ◁ C2×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31620

Conjugacy classes & character table

7998 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 18);