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C5×(C31⋊C9)⋊Dic5 #42124352

order27900
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C31⋊C9)⋊Dic5
unambiguous semidirect product(C5×Dic155)⋊C9

Splittings

derivedC5×C31 ⋊ C4×C5×C9
HallC52×C31⋊C9 ⋊ C4
HallC5×Dic155 ⋊ C9
HallC52×C31 ⋊ C4×C9
HallC31⋊C9 ⋊ C5×Dic5
SylowC31 ⋊ C5×C9×Dic5
SylowC52 ⋊ Dic31⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C5⋊(D31⋊C3)
commutator, hypocenterC5×C31C4×C5×C9
FrattiniC2×C3C5×C5⋊(D31⋊C3)
Fitting, socle, prime radicalC2×C3×C52×C31C2×C3
cosocleC2×C3×C5×C31C2×C3×C5
LCSG ▷ C5×C31
UCSC1 ◁ C2×C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 99);