Finite Group Databasebeta

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C5×Dic15×C31⋊C3 #42124635

order27900
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic15×C31⋊C3
unambiguous semidirect productC3⋊(C5×Dic5×C31⋊C3)
unambiguous semidirect product(C5×C31×Dic15)⋊C3

Splittings

derivedC3×C5×C31 ⋊ C3×C4×C5
HallC3×C52×C31⋊C3 ⋊ C4
HallC52×C31 ⋊ C3×Dic3
HallC3×C31⋊C3 ⋊ C5×Dic5
SylowC31 ⋊ C3×C5×Dic15
SylowC52 ⋊ Dic3×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5D15×C31⋊C3
commutator, hypocenterC3×C5×C31C3×C4×C5
FrattiniC2C5×D15×C31⋊C3
Fitting, socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C52×C31⋊C3C2
cosocleC2×C3×C5×C31C2×C3×C5
LCSG ▷ C3×C5×C31
UCSC1 ◁ C2×C5

160 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 54 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

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 382);