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C5×#17987952 #37552032

order23310
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×#17987952

Splittings

Fitting, socle, HallC5×C7×C37 ⋊ C2×C9
derived, HallC7×C37 ⋊ C2×C5×C9
HallC5×#14556422 ⋊ C2
HallC5×D259 ⋊ C9
Hall#14556422 ⋊ C2×C5
HallD259 ⋊ C5×C9
HallC5×C37 ⋊ D7⋊C9
SylowC37 ⋊ C5×D7⋊C9
HallC5×C7 ⋊ #66526⋊C2
SylowC7 ⋊ C5×#66526⋊C2

Subgroups

subgroupG/H
center, hypercenterC5#17987952
commutator, hypocenterC7×C37C2×C5×C9
FrattiniC1G
Fitting, socleC5×C7×C37C2×C9
prime radicalC5×(C37⋊C3)⋊D7C3
cosocleC7×C37⋊C3C2×C3×C5
LCSG ▷ C7×C37
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1295

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 51);