Finite Group Databasebeta

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C32×Dic1045 #49178495

order37620
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC32×Dic1045
unambiguous semidirect productC11⋊(C32×Dic95)

Splittings

derived, HallC5×C11×C19 ⋊ C32×C4
HallC32×C5×C11×C19 ⋊ C4
HallC32×C11×C19 ⋊ Dic5
HallC32×C5×C19 ⋊ Dic11
HallC32×C5×C11 ⋊ Dic19
HallC11×C19 ⋊ C32×Dic5
HallC32×C19 ⋊ Dic55
HallC32×C11 ⋊ Dic95
HallC5×C19 ⋊ C32×Dic11
HallC5×C11 ⋊ C32×Dic19
HallC32×C5 ⋊ Dic209
SylowC19 ⋊ C32×Dic55
SylowC11 ⋊ C32×Dic95
SylowC5 ⋊ C32×Dic209

Subgroups

subgroupG/H
center, hypercenterC2×C32D1045
commutator, hypocenterC5×C11×C19C32×C4
FrattiniC2C32×D1045
Fitting, socle, prime radicalC2×C32×C5×C11×C19C2
cosocleC2×C5×C11×C19C2×C32
LCSG ▷ C5×C11×C19
UCSC1 ◁ C2×C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

9432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 204);