Finite Group Databasebeta

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C2×C7×C3⋊(C5⋊D35) #28413575

order14700
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C7×C3⋊(C5⋊D35)
unambiguous semidirect product(C2×C3)⋊(C7×C5⋊D35)
unambiguous semidirect product(C2×C5)⋊(C7×D105)
unambiguous semidirect product(C2×C7)⋊(C7×C3⋊(C5⋊D5))

Splittings

Fitting, socleC2×C3×C52×C72 ⋊ C2
derivedC3×C52×C7 ⋊ C22×C7
HallC3×C52×C72 ⋊ C22
HallC52×C72 ⋊ C2×D3
HallC3×C72 ⋊ C2×C5⋊D5
HallC3×C52 ⋊ C2×C7×D7
SylowC72 ⋊ C2×C3⋊(C5⋊D5)
SylowC52 ⋊ C2×C7×D21
SylowC3 ⋊ C2×C7×C5⋊D35

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C5⋊D35)
commutator, cosocle, hypocenterC3×C52×C7C22×C7
FrattiniC1G
Fitting, socleC2×C3×C52×C72C2
LCSG ▷ C3×C52×C7
UCSC1 ◁ C2×C7

416 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 134 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

3696 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 754);