Finite Group Databasebeta

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C3×D5×D385 #37528618

order23100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×D385
unambiguous semidirect product(C5×D5)⋊(C3×D77)
unambiguous semidirect product(D5×C11)⋊(C3×D35)

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C22
derived, HallC52×C7×C11 ⋊ C22×C3
HallC3×C52×C11 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D11
HallC52×C11 ⋊ C2×C3×D7
HallC3×C7×C11 ⋊ D52
HallC52×C7 ⋊ C2×C3×D11
HallC7×C11 ⋊ C3×D52
HallC3×C52 ⋊ C2×D77
HallC3×C11 ⋊ D5×D35
SylowC52 ⋊ C2×C3×D77
HallC3×C7 ⋊ D5×D55
SylowC11 ⋊ C3×D5×D35
SylowC7 ⋊ C3×D5×D55

Subgroups

subgroupG/H
center, hypercenterC3D5×D385
commutator, cosocle, hypocenterC52×C7×C11C22×C3
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C52×C7×C11
UCSC1 ◁ C3

192 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 56 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) = 2310

Conjugacy classes & character table

2328 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 429);