Finite Group Databasebeta

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C5×#17987932 #37552005

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

Aliases

direct productC5×#17987932

Splittings

derived, HallC7×C37 ⋊ C2×C5×C9
HallC5×#14556418 ⋊ C2
HallC5×C7×D37 ⋊ C9
Hall#14556418 ⋊ C2×C5
HallC5×C7×C37 ⋊ C2×C9
HallC7×D37 ⋊ C5×C9
HallC5×D37 ⋊ C7⋊C9
HallC5×C37 ⋊ C2×C7⋊C9
HallD37 ⋊ C5×C7⋊C9
SylowC37 ⋊ C2×C5×C7⋊C9
HallC5×C7 ⋊ #66524⋊C2
SylowC7 ⋊ C5×#66524⋊C2

Subgroups

subgroupG/H
center, hypercenterC3×C5#13095532
commutator, hypocenterC7×C37C2×C5×C9
FrattiniC3C5×#13095532
Fitting, socleC3×C5×C7×C37C2×C3
prime radicalC3×C5×C7×D37C3
cosocleC3×C7×C37C2×C3×C5
LCSG ▷ C7×C37
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 24);