Finite Group Databasebeta

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C2×C25×D279 #42124306

order27900
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×D279
unambiguous semidirect product(C2×C9)⋊(C25×D31)

Splittings

FittingC2×C9×C25×C31 ⋊ C2
derived, HallC9×C31 ⋊ C22×C25
HallC9×C25×C31 ⋊ C22
HallC25×C31 ⋊ C2×D9
HallC9×C25 ⋊ C2×D31
SylowC31 ⋊ C2×D9×C25
SylowC9 ⋊ C2×C25×D31

Subgroups

subgroupG/H
center, hypercenterC2×C25D279
commutator, hypocenterC9×C31C22×C25
FrattiniC3×C5C2×C5×D93
FittingC2×C9×C25×C31C2
socleC2×C3×C5×C31C5×D3
prime radicalC2×C5×D279C5
cosocleC5×C9×C31C22×C5
LCSG ▷ C9×C31
UCSC1 ◁ C2×C25

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 53);