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C2×C3⋊(D31⋊C25) #22604756

order9300
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(D31⋊C25)
unambiguous semidirect product(C2×C3)⋊(D31⋊C25)
unambiguous semidirect product(C2×D93)⋊C25
unambiguous semidirect product(C2×C31⋊C25)⋊D3

Splittings

derived, HallC3×C31 ⋊ C22×C25
HallC3×C31⋊C25 ⋊ C22
HallC31⋊C25 ⋊ C2×D3
HallC2×D93 ⋊ C25
SylowC31 ⋊ C2×D3×C25
SylowC3 ⋊ C2×D31⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(D31⋊C5)
commutator, hypocenterC3×C31C22×C25
FrattiniC5C2×C3⋊(D31⋊C5)
Fitting, socleC2×C3×C5×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C2×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C9⋊(D31⋊C25), C2×C3⋊((D31⋊C3)⋊C25), D3×C3⋊(D31⋊C25), …
maximal normal subgroup ofC2×C3⋊((D31⋊C3)⋊C25), C2×C3×C3⋊(D31⋊C25)
maximal quotient ofC2×C9⋊(D31⋊C25), D3×C3⋊(D31⋊C25), C2×C3×C3⋊(D31⋊C25), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 30);