Finite Group Databasebeta

← Prev (#22603326) Next (#22603328) →

C2×C5×D455 #22603327

order9100
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D455
unambiguous semidirect product(C2×C5)⋊(C5×D91)
unambiguous semidirect product(C2×C7)⋊(C5×D65)
unambiguous semidirect product(C2×C13)⋊(C5×D35)

Splittings

Fitting, socleC2×C52×C7×C13 ⋊ C2
derivedC5×C7×C13 ⋊ C22×C5
HallC52×C7×C13 ⋊ C22
HallC52×C13 ⋊ C2×D7
HallC52×C7 ⋊ C2×D13
HallC7×C13 ⋊ C2×C5×D5
SylowC52 ⋊ C2×D91
SylowC13 ⋊ C2×C5×D35
SylowC7 ⋊ C2×C5×D65

Subgroups

subgroupG/H
center, hypercenterC2×C5D455
commutator, hypocenterC5×C7×C13C22×C5
FrattiniC1G
Fitting, socleC2×C52×C7×C13C2
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2290 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7⋊(C13⋊#3874), C2×C5×C5⋊#10587722, C2×C5×C5⋊#10587723, …
maximal normal subgroup ofC2×C5×C5⋊#10587722, C2×C5×C5⋊#10587723, C2×C5×C5⋊(ΓL(1,𝔽8)⋊D13), …
maximal quotient ofC5×D3×D455, C2×C3×C5×D455, C2×C5×D1365

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9100, 112);