Finite Group Databasebeta

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C2×C52×D31⋊C9 #42124522

order27900
automorphism?
homologyAbelianization (H1) = C22×C52×C9 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×D31⋊C9

Splittings

derived, SylowC31 ⋊ C22×C52×C9
HallC52×C31⋊C9 ⋊ C22
HallC2×C52×D31 ⋊ C9
HallC52×C31 ⋊ C22×C9
HallC31⋊C9 ⋊ C22×C52
HallC2×D31 ⋊ C52×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C52D31⋊C3
commutator, hypocenterC31C22×C52×C9
FrattiniC3C2×C52×D31⋊C3
Fitting, socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C52×D31C3
cosocleC3×C31C22×C3×C52
LCSG ▷ C31
UCSC1 ◁ C2×C3×C52

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 269);