Finite Group Databasebeta

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C2×C5×D15×C121 #49137013

order36300
automorphism?
homologyAbelianization (H1) = C22×C5×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D15×C121
unambiguous semidirect product(C2×C3)⋊(C5×D5×C121)
unambiguous semidirect product(C2×C5)⋊(C5×D3×C121)

Splittings

FittingC2×C3×C52×C121 ⋊ C2
derivedC3×C5 ⋊ C22×C5×C121
HallC3×C52×C121 ⋊ C22
HallC52×C121 ⋊ C2×D3
HallC3×C121 ⋊ C2×C5×D5
HallC3×C52 ⋊ C22×C121
SylowC52 ⋊ C2×D3×C121
SylowC3 ⋊ C2×C5×D5×C121

Subgroups

subgroupG/H
center, hypercenterC2×C5×C121D15
commutator, hypocenterC3×C5C22×C5×C121
FrattiniC11C2×C5×C11×D15
FittingC2×C3×C52×C121C2
socleC2×C3×C52×C11C2×C11
prime radicalC2×C5×C11×D15C11
cosocleC3×C5×C11C22×C5×C11
LCSG ▷ C3×C5
UCSC1 ◁ C2×C5×C121

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

normal subgroups only

This group has 144 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) = 7260

Conjugacy classes & character table

10890 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 149);