Finite Group Databasebeta

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C2×C3×C5×D95 #19152899

order5700
isoclinismisoclinic class of D95
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D95
unambiguous semidirect product(C2×C5)⋊(C3×C5×D19)

Splittings

Fitting, socleC2×C3×C52×C19 ⋊ C2
derivedC5×C19 ⋊ C22×C3×C5
HallC3×C52×C19 ⋊ C22
HallC52×C19 ⋊ C22×C3
HallC3×C52 ⋊ C2×D19
HallC3×C19 ⋊ C2×C5×D5
SylowC52 ⋊ C2×C3×D19
SylowC19 ⋊ C2×C3×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D95
commutator, hypocenterC5×C19C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C52×C19C2
LCSG ▷ C5×C19
UCSC1 ◁ C2×C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C5⋊(#4294⋊C2), C2×C5×C9×D95, C2×C3×C5×C5⋊(D19⋊C3), …
maximal normal subgroup ofC2×C5×C5⋊(#4294⋊C2), C2×C5×C9×D95, C2×C3×C5×C5⋊(D19⋊C3), …
maximal quotient ofC2×C5×C9×D95, C3×C5×D3×D95, C2×C3×C5×D285, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 156);