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C52×C22⋊(C31⋊C3) #22604930

order9300
isoclinismisoclinic class of C22⋊(C31⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×C22⋊(C31⋊C3)
unambiguous semidirect productC22⋊(C52×C31⋊C3)
unambiguous semidirect product(C22×C5)⋊(C5×C31⋊C3)

Splittings

Fitting, socle, HallC22×C52×C31 ⋊ C3
derived, HallC22×C31 ⋊ C3×C52
HallC52×C31 ⋊ A4
HallC22×C52 ⋊ C31⋊C3
SylowC31 ⋊ C52×A4
SylowC22 ⋊ C52×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC52C22⋊(C31⋊C3)
commutator, hypocenterC22×C31C3×C52
FrattiniC1G
Fitting, socleC22×C52×C31C3
LCSG ▷ C22×C31
UCSC1 ◁ C52

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC52⋊C3×C22⋊(C31⋊C3), (C22⋊(C52⋊C3))⋊(C31⋊C3), C52×A4×C31⋊C3, …
maximal normal subgroup ofC52⋊C3×C22⋊(C31⋊C3), (C22⋊(C52⋊C3))⋊(C31⋊C3), C52×A4×C31⋊C3, …
maximal quotient ofC52×C22⋊(C31⋊C9), C3×C52×C22⋊(C31⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 204);