Finite Group Databasebeta

← Prev (#37552014) Next (#37552016) →

D5×C37×C7⋊C9 #37552015

order23310
automorphism?
homologyAbelianization (H1) = C2×C9×C37 · Schur multiplier (H2) = C1

Aliases

direct productD5×C37×C7⋊C9
unambiguous semidirect productC5⋊(C2×C37×C7⋊C9)
unambiguous semidirect product(C7×D5)⋊(C9×C37)

Splittings

derived, HallC5×C7 ⋊ C2×C9×C37
HallC5×C37×C7⋊C9 ⋊ C2
HallC7×D5×C37 ⋊ C9
HallC5×C7×C37 ⋊ C2×C9
HallC5×C7⋊C9 ⋊ C2×C37
HallC7×C37 ⋊ C9×D5
HallC5×C37 ⋊ C2×C7⋊C9
HallC7×D5 ⋊ C9×C37
SylowC7 ⋊ C9×D5×C37
SylowC5 ⋊ C2×C37×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C37D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C2×C9×C37
FrattiniC3D5×ΓL(1,𝔽8)×C37
Fitting, socleC3×C5×C7×C37C2×C3
prime radicalC3×C7×D5×C37C3
cosocleC3×C5×C7C2×C3×C37
LCSG ▷ C5×C7
UCSC1 ◁ C3×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

2220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 34);