Finite Group Databasebeta

← Prev (#22604875) Next (#22604877) →

C2×C5×C5⋊(D31⋊C3) #22604876

order9300
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C5⋊(D31⋊C3)
unambiguous semidirect product(C2×C5)⋊(C5×D31⋊C3)
unambiguous semidirect product(C2×C5×D155)⋊C3

Splittings

Fitting, socleC2×C52×C31 ⋊ C2×C3
derivedC5×C31 ⋊ C22×C3×C5
HallC2×C5×D155 ⋊ C3
HallC52×C31⋊C3 ⋊ C22
HallC52×C31 ⋊ C22×C3
HallC31⋊C3 ⋊ C2×C5×D5
SylowC31 ⋊ C2×C3×C5×D5
SylowC52 ⋊ C2×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C5⋊(D31⋊C3)
commutator, hypocenterC5×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C52×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

370 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C31⋊C3)⋊#3874, C5×D3×C5⋊(D31⋊C3), C2×C3×C5×C5⋊(D31⋊C3), …
maximal normal subgroup ofC2×C3×C5×C5⋊(D31⋊C3)
maximal quotient ofC2×C5×C5⋊(D31⋊C9), C5×D3×C5⋊(D31⋊C3), C2×C3×C5×C5⋊(D31⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 150);