Finite Group Databasebeta

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C2×C5×D735 #28413017

order14700
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D735
unambiguous semidirect product(C2×C3)⋊(C5×D245)
unambiguous semidirect product(C2×C5)⋊(C5×D147)
unambiguous semidirect product(C2×C49)⋊(C5×D15)

Splittings

FittingC2×C3×C52×C49 ⋊ C2
derivedC3×C5×C49 ⋊ C22×C5
HallC3×C52×C49 ⋊ C22
HallC52×C49 ⋊ C2×D3
HallC3×C49 ⋊ C2×C5×D5
HallC3×C52 ⋊ C2×D49
SylowC49 ⋊ C2×C5×D15
SylowC52 ⋊ C2×D147
SylowC3 ⋊ C2×C5×D245

Subgroups

subgroupG/H
center, hypercenterC2×C5D735
commutator, cosocle, hypocenterC3×C5×C49C22×C5
FrattiniC7C2×C5×D105
FittingC2×C3×C52×C49C2
socleC2×C3×C52×C7D7
LCSG ▷ C3×C5×C49
UCSC1 ◁ C2×C5

144 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

3690 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 196);