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C31×C9⋊#1039 #42124377

order27900
automorphism?
homologyAbelianization (H1) = C4×C31 · Schur multiplier (H2) = C5

Aliases

direct productC31×C9⋊#1039
unambiguous semidirect productC9⋊(C31×#1039)

Splittings

derived, HallC52×C9 ⋊ C4×C31
HallC52×C9×C31 ⋊ C4
HallC52×C31 ⋊ Dic9
HallC9×C31 ⋊ #1039
SylowC52 ⋊ C31×Dic9
SylowC9 ⋊ C31×#1039

Subgroups

subgroupG/H
center, hypercenterC2×C31C5⋊D45
commutator, hypocenterC52×C9C4×C31
FrattiniC2×C3C31×C3⋊(C5⋊D5)
FittingC2×C52×C9×C31C2
socle, prime radicalC2×C3×C52×C31D3
cosocleC2×C52×C9C2×C31
LCSG ▷ C52×C9
UCSC1 ◁ C2×C31

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7068 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 124);