Finite Group Databasebeta

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C2×C5×C3⋊D105 #20263158

order6300
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C3⋊D105
unambiguous semidirect product(C2×C3)⋊(C5×D105)
unambiguous semidirect product(C2×C5)⋊(C5×C3⋊D21)
unambiguous semidirect product(C2×C7)⋊(C5×C3⋊D15)

Splittings

Fitting, socleC2×C32×C52×C7 ⋊ C2
derivedC32×C5×C7 ⋊ C22×C5
HallC32×C52×C7 ⋊ C22
HallC32×C52 ⋊ C2×D7
HallC52×C7 ⋊ C2×C3⋊D3
HallC32×C7 ⋊ C2×C5×D5
SylowC52 ⋊ C2×C3⋊D21
SylowC32 ⋊ C2×C5×D35
SylowC7 ⋊ C2×C5×C3⋊D15

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D105
commutator, hypocenterC32×C5×C7C22×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C32×C5×C7
UCSC1 ◁ C2×C5

288 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 102 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

1590 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6300, 554);