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C5×Dic1771 #47978376

order35420
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic1771
unambiguous semidirect productC7⋊(C5×Dic253)
unambiguous semidirect productC23⋊(C5×Dic77)

Splittings

derived, HallC7×C11×C23 ⋊ C4×C5
HallC5×C7×C11×C23 ⋊ C4
HallC5×C11×C23 ⋊ Dic7
HallC5×C7×C23 ⋊ Dic11
HallC5×C7×C11 ⋊ Dic23
HallC11×C23 ⋊ C5×Dic7
HallC7×C23 ⋊ C5×Dic11
HallC5×C23 ⋊ Dic77
HallC7×C11 ⋊ C5×Dic23
HallC5×C11 ⋊ Dic161
HallC5×C7 ⋊ Dic253
SylowC23 ⋊ C5×Dic77
SylowC11 ⋊ C5×Dic161
SylowC7 ⋊ C5×Dic253

Subgroups

subgroupG/H
center, hypercenterC2×C5D1771
commutator, hypocenterC7×C11×C23C4×C5
FrattiniC2C5×D1771
Fitting, socle, prime radicalC2×C5×C7×C11×C23C2
cosocleC2×C7×C11×C23C2×C5
LCSG ▷ C7×C11×C23
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35420

Conjugacy classes & character table

8870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 10);