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C2×C5⋊(C5⋊(D31⋊C3)) #22604878

order9300
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5⋊(C5⋊(D31⋊C3))
unambiguous semidirect product(C2×C5)⋊(C5⋊(D31⋊C3))
unambiguous semidirect product(C2×C31⋊C3)⋊(C5⋊D5)

Splittings

Fitting, socleC2×C52×C31 ⋊ C2×C3
derived, HallC52×C31 ⋊ C22×C3
HallC2×C5⋊D155 ⋊ C3
HallC52×C31⋊C3 ⋊ C22
HallC31⋊C3 ⋊ C2×C5⋊D5
SylowC31 ⋊ C2×C3×C5⋊D5
SylowC52 ⋊ C2×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C5⋊(D31⋊C3))
commutator, hypocenterC52×C31C22×C3
FrattiniC1G
Fitting, socleC2×C52×C31C2×C3
LCSG ▷ C52×C31
UCSC1 ◁ C2

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

334 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C31⋊C3)⋊((C5⋊D5)⋊C3), D3×C5⋊(C5⋊(D31⋊C3)), C2×C3×C5⋊(C5⋊(D31⋊C3)), …
maximal normal subgroup ofC2×(C31⋊C3)⋊((C5⋊D5)⋊C3), C2×C3×C5⋊(C5⋊(D31⋊C3))
maximal quotient ofC2×C5⋊(C5⋊(D31⋊C9)), D3×C5⋊(C5⋊(D31⋊C3)), C2×C3×C5⋊(C5⋊(D31⋊C3)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 152);