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C31×C22⋊(C52⋊C3) #22604929

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

Aliases

direct productC31×C22⋊(C52⋊C3)
unambiguous semidirect productC22⋊(C31×C52⋊C3)
unambiguous semidirect productC52⋊(A4×C31)

Splittings

Fitting, socle, HallC22×C52×C31 ⋊ C3
derived, HallC22×C52 ⋊ C3×C31
HallC52×C31 ⋊ A4
HallC22×C31 ⋊ C52⋊C3
SylowC52 ⋊ A4×C31
SylowC22 ⋊ C31×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC31C22⋊(C52⋊C3)
commutator, hypocenterC22×C52C3×C31
FrattiniC1G
Fitting, socleC22×C52×C31C3
LCSG ▷ C22×C52
UCSC1 ◁ C31

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1116 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC31⋊C3×C22⋊(C52⋊C3), A4×C31×C52⋊C3, (C22⋊(C52⋊C3))⋊(C31⋊C3), …
maximal normal subgroup ofC31⋊C3×C22⋊(C52⋊C3), A4×C31×C52⋊C3, (C22⋊(C52⋊C3))⋊(C31⋊C3), …
maximal quotient ofC31×C22⋊(C52⋊C9), C3×C31×C22⋊(C52⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 203);