Finite Group Databasebeta

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C2×C5×C31×C3⋊D15 #42124993

order27900
isoclinismisoclinic class of C3⋊D15
automorphism?
homologyAbelianization (H1) = C22×C5×C31 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C31×C3⋊D15
unambiguous semidirect product(C2×C3)⋊(C5×D15×C31)
unambiguous semidirect product(C2×C5)⋊(C5×C3⋊D3×C31)

Splittings

Fitting, socleC2×C32×C52×C31 ⋊ C2
derivedC32×C5 ⋊ C22×C5×C31
HallC32×C52×C31 ⋊ C22
HallC52×C31 ⋊ C2×C3⋊D3
HallC32×C31 ⋊ C2×C5×D5
HallC32×C52 ⋊ C22×C31
SylowC52 ⋊ C2×C3⋊D3×C31
SylowC32 ⋊ C2×C5×D5×C31

Subgroups

subgroupG/H
center, hypercenterC2×C5×C31C3⋊D15
commutator, cosocle, hypocenterC32×C5C22×C5×C31
FrattiniC1G
Fitting, socleC2×C32×C52×C31C2
LCSG ▷ C32×C5
UCSC1 ◁ C2×C5×C31

288 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 108 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

7440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 740);