Finite Group Databasebeta

← Prev (#20301661) Next (#20301663) →

C2×C5×C3⋊D123 #20301662

order7380
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C3⋊D123
unambiguous semidirect product(C2×C3)⋊(C5×D123)

Splittings

Fitting, socleC2×C32×C5×C41 ⋊ C2
derived, HallC32×C41 ⋊ C22×C5
HallC32×C5×C41 ⋊ C22
HallC5×C41 ⋊ C2×C3⋊D3
HallC32×C5 ⋊ C2×D41
SylowC41 ⋊ C2×C5×C3⋊D3
SylowC32 ⋊ C2×C5×D41

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D123
commutator, hypocenterC32×C41C22×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C41C2
LCSG ▷ C32×C41
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1860 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3⋊(C3⋊(D41⋊C25)), C2×C25×C3⋊D123, C2×C5×C3⋊(C3⋊(D41⋊C5)), …
maximal normal subgroup ofC2×C3⋊(C3⋊(D41⋊C25)), C2×C25×C3⋊D123, C2×C5×C3⋊(C3⋊(D41⋊C5)), …
maximal quotient ofC2×C25×C3⋊D123, C5×D5×C3⋊D123, C2×C52×C3⋊D123, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 140);