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C22×C5×(C31⋊C3)⋊C5 #22604840

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

Aliases

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

Splittings

Fitting, socleC22×C5×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C22×C3×C52
HallC22×C5×ΓL(1,𝔽32) ⋊ C3
HallC5×ΓL(1,𝔽32) ⋊ C22×C3
HallC22×C31⋊C3 ⋊ C52
HallC22×C31 ⋊ C3×C52
HallC31⋊C3 ⋊ C22×C52

Subgroups

subgroupG/H
center, hypercenterC22×C5(C31⋊C3)⋊C5
commutator, hypocenterC31C22×C3×C52
FrattiniC1G
Fitting, socleC22×C5×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C22×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

340 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×A4×(C31⋊C3)⋊C5, C2×C5×D3×(C31⋊C3)⋊C5, C22×C3×C5×(C31⋊C3)⋊C5
maximal normal subgroup ofC5×A4×(C31⋊C3)⋊C5, C22×C3×C5×(C31⋊C3)⋊C5
maximal quotient ofC22×C5×ΓL(1,𝔽32)⋊C9, C2×C5×D3×(C31⋊C3)⋊C5, C22×C3×C5×(C31⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 114);