Finite Group Databasebeta

← Prev (#22576501) Next (#22576503) →

C2×C3×C5⋊D145 #22576502

order8700
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C3×C5⋊D145
unambiguous semidirect product(C2×C5)⋊(C3×D145)
unambiguous semidirect product(C2×C29)⋊(C3×C5⋊D5)

Splittings

Fitting, socleC2×C3×C52×C29 ⋊ C2
derived, HallC52×C29 ⋊ C22×C3
HallC3×C52×C29 ⋊ C22
HallC3×C29 ⋊ C2×C5⋊D5
HallC3×C52 ⋊ C2×D29
SylowC29 ⋊ C2×C3×C5⋊D5
SylowC52 ⋊ C2×C3×D29

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊D145
commutator, hypocenterC52×C29C22×C3
FrattiniC1G
Fitting, socleC2×C3×C52×C29C2
LCSG ▷ C52×C29
UCSC1 ◁ C2×C3

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C29⋊((C5⋊D5)⋊C9), C2×C9×C5⋊D145, C2×C3×C29⋊((C5⋊D5)⋊C3), …
maximal normal subgroup ofC2×C29⋊((C5⋊D5)⋊C9), C2×C9×C5⋊D145, C2×C3×C29⋊((C5⋊D5)⋊C3), …
maximal quotient ofC2×C9×C5⋊D145, C3×D3×C5⋊D145, C2×C32×C5⋊D145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8700, 144);