Finite Group Databasebeta

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C3⋊D15×D161 #44394641

order28980
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3⋊D15×D161

Splittings

Fitting, socle, derived, HallC32×C5×C7×C23 ⋊ C22
HallC32×C7×C23 ⋊ C2×D5
HallC32×C5×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D23
HallC32×C23 ⋊ D5×D7
HallC7×C23 ⋊ C2×C3⋊D15
HallC5×C23 ⋊ D7×C3⋊D3
HallC32×C7 ⋊ D5×D23
HallC32×C5 ⋊ C2×D161
HallC5×C7 ⋊ C3⋊D3×D23
SylowC23 ⋊ D7×C3⋊D15
SylowC32 ⋊ D5×D161
SylowC7 ⋊ D23×C3⋊D15
SylowC5 ⋊ C3⋊D3×D161

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C23C22
LCSG ▷ C32×C5×C7×C23
UCSC1

240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 7245

Conjugacy classes & character table

1968 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 310);