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C5×Dic1395 #42124376

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

Aliases

direct productC5×Dic1395
unambiguous semidirect productC9⋊(C5×Dic155)

Splittings

derivedC5×C9×C31 ⋊ C4×C5
HallC52×C9×C31 ⋊ C4
HallC52×C31 ⋊ Dic9
HallC9×C31 ⋊ C5×Dic5
HallC52×C9 ⋊ Dic31
SylowC31 ⋊ C5×Dic45
SylowC52 ⋊ Dic279
SylowC9 ⋊ C5×Dic155

Subgroups

subgroupG/H
center, hypercenterC2×C5D1395
commutator, hypocenterC5×C9×C31C4×C5
FrattiniC2×C3C5×D465
FittingC2×C52×C9×C31C2
socle, prime radicalC2×C3×C52×C31D3
cosocleC2×C5×C9×C31C2×C5
LCSG ▷ C5×C9×C31
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6990 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 123);