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D31×C3⋊(C5⋊D5) #22604916

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

Aliases

direct productD31×C3⋊(C5⋊D5)
unambiguous semidirect product(C3×D31)⋊(C5⋊D5)
unambiguous semidirect product(C5×D31)⋊D15

Splittings

Fitting, socle, derived, HallC3×C52×C31 ⋊ C22
HallC52×C31 ⋊ C2×D3
HallC3×C31 ⋊ C2×C5⋊D5
HallC3×C52 ⋊ C2×D31
SylowC31 ⋊ C2×C3⋊(C5⋊D5)
SylowC52 ⋊ D3×D31
SylowC3 ⋊ C5⋊D5×D31

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C52×C31C22
LCSG ▷ C3×C52×C31
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

663 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD31×C5⋊D45, D31⋊(C3⋊((C5⋊D5)⋊C3)), D31×C3⋊((C5⋊D5)⋊C3), …
maximal normal subgroup ofD31⋊(C3⋊((C5⋊D5)⋊C3)), D31×C3⋊((C5⋊D5)⋊C3), C3⋊(C5⋊D5)×D31⋊C3, …
maximal quotient ofD31×C5⋊D45, C3×D31×C3⋊(C5⋊D5), D93⋊(C3⋊(C5⋊D5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 190);