Finite Group Databasebeta

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C2×C9×C25×D31 #42124302

order27900
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C22×C9×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C25×D31

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C9×C25D31
commutator, hypocenterC31C22×C9×C25
FrattiniC3×C5C2×C3×C5×D31
FittingC2×C9×C25×C31C2
socleC2×C3×C5×C31C2×C3×C5
prime radicalC2×C3×C5×D31C3×C5
cosocleC3×C5×C31C22×C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C9×C25

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 49);