Finite Group Databasebeta

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C22×C31×C52⋊C9 #42124580

order27900
isoclinismisoclinic class of C52⋊C3
automorphism?
homologyAbelianization (H1) = C22×C9×C31 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C31×C52⋊C9

Splittings

derived, SylowC52 ⋊ C22×C9×C31
HallC22×C52×C31 ⋊ C9
HallC52×C31 ⋊ C22×C9
HallC22×C52 ⋊ C9×C31

Subgroups

subgroupG/H
center, hypercenterC22×C3×C31C52⋊C3
commutator, hypocenterC52C22×C9×C31
FrattiniC3C22×C31×C52⋊C3
Fitting, socle, prime radicalC22×C3×C52×C31C3
cosocleC3×C52C22×C3×C31
LCSG ▷ C52
UCSC1 ◁ C22×C3×C31

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 327);