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C52×C31×Dic9 #42124373

order27900
isoclinismisoclinic class of D9
automorphism?
homologyAbelianization (H1) = C4×C52×C31 · Schur multiplier (H2) = C5

Aliases

direct productC52×C31×Dic9
unambiguous semidirect productC9⋊(C4×C52×C31)

Splittings

derived, SylowC9 ⋊ C4×C52×C31
HallC52×C9×C31 ⋊ C4
HallC9×C31 ⋊ C4×C52
HallC52×C9 ⋊ C4×C31

Subgroups

subgroupG/H
center, hypercenterC2×C52×C31D9
commutator, hypocenterC9C4×C52×C31
FrattiniC2×C3C52×D3×C31
FittingC2×C52×C9×C31C2
socle, prime radicalC2×C3×C52×C31D3
cosocleC2×C9C2×C52×C31
LCSG ▷ C9
UCSC1 ◁ C2×C52×C31

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 120);