Finite Group Databasebeta

← Prev (#22604943) Next (#22604945) →

C2×C3×C5×D5×C31 #22604944

order9300
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D5×C31
unambiguous semidirect productC5⋊(C22×C3×C5×C31)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C5×C31)

Splittings

Fitting, socleC2×C3×C52×C31 ⋊ C2
derivedC5 ⋊ C22×C3×C5×C31
HallC3×C52×C31 ⋊ C22
HallC52×C31 ⋊ C22×C3
HallC3×C52 ⋊ C22×C31
SylowC52 ⋊ C22×C3×C31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C31D5
commutator, hypocenterC5C22×C3×C5×C31
FrattiniC1G
Fitting, socleC2×C3×C52×C31C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C5×C31

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×D5×C31⋊C9, C2×C5×C9×D5×C31, C2×C3×C31×#3874, …
maximal normal subgroup ofC2×C5×D5×C31⋊C9, C2×C5×C9×D5×C31, C2×C3×C5×D5×C31⋊C3, …
maximal quotient ofC2×C5×C9×D5×C31, C3×C5×D3×D5×C31, C2×C32×C5×D5×C31, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 218);