Finite Group Databasebeta

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C2×C3×C3⋊(C5⋊D35) #20263162

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

Aliases

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

Splittings

Fitting, socleC2×C32×C52×C7 ⋊ C2
derivedC3×C52×C7 ⋊ C22×C3
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×C3×C3⋊(C5⋊D5)

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C5⋊D35)
commutator, hypocenterC3×C52×C7C22×C3
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C3×C52×C7
UCSC1 ◁ C2×C3

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

normal subgroups only

This group has 352 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

1584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6300, 558);