Finite Group Databasebeta

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C2×C3×C7×D385 #44568940

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D385
unambiguous semidirect product(C2×C5)⋊(C3×C7×D77)
unambiguous semidirect product(C2×C11)⋊(C3×C7×D35)

Splittings

Fitting, socleC2×C3×C5×C72×C11 ⋊ C2
derivedC5×C7×C11 ⋊ C22×C3×C7
HallC3×C5×C72×C11 ⋊ C22
HallC5×C72×C11 ⋊ C22×C3
HallC3×C72×C11 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D11
HallC72×C11 ⋊ C2×C3×D5
HallC5×C72 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C2×C7×D7
HallC3×C72 ⋊ C2×D55
HallC5×C11 ⋊ C2×C3×C7×D7
SylowC72 ⋊ C2×C3×D55
HallC3×C11 ⋊ C2×C7×D35
HallC3×C5 ⋊ C2×C7×D77
SylowC11 ⋊ C2×C3×C7×D35
SylowC5 ⋊ C2×C3×C7×D77

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D385
commutator, cosocle, hypocenterC5×C7×C11C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C5×C7×C11
UCSC1 ◁ C2×C3×C7

208 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

8148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 642);