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C32×C19×Dic55 #49178496

order37620
automorphism?
homologyAbelianization (H1) = C32×C4×C19 · Schur multiplier (H2) = C3

Aliases

direct productC32×C19×Dic55
unambiguous semidirect productC11⋊(C32×C19×Dic5)

Splittings

derived, HallC5×C11 ⋊ C32×C4×C19
HallC32×C5×C11×C19 ⋊ C4
HallC32×C11×C19 ⋊ Dic5
HallC5×C11×C19 ⋊ C32×C4
HallC32×C5×C19 ⋊ Dic11
HallC32×C5×C11 ⋊ C4×C19
HallC11×C19 ⋊ C32×Dic5
HallC32×C11 ⋊ C19×Dic5
HallC5×C19 ⋊ C32×Dic11
HallC32×C5 ⋊ C19×Dic11
SylowC11 ⋊ C32×C19×Dic5
SylowC5 ⋊ C32×C19×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C32×C19D55
commutator, hypocenterC5×C11C32×C4×C19
FrattiniC2C32×C19×D55
Fitting, socle, prime radicalC2×C32×C5×C11×C19C2
cosocleC2×C5×C11C2×C32×C19
LCSG ▷ C5×C11
UCSC1 ◁ C2×C32×C19

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

9918 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 205);