Finite Group Databasebeta

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C2×C5⋊#10624391 #20300076

order7260
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊#10624391
unambiguous semidirect product(C2×C5)⋊#10624391

Splittings

Fitting, socleC2×C5×C112 ⋊ D3
derived, HallC5×C112⋊C3 ⋊ C22
HallC5×C112 ⋊ C2×D3
HallC112⋊C3 ⋊ C2×D5
SylowC112 ⋊ C2×D15
SylowC5 ⋊ C2×#10624391

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#10624391
commutator, hypocenterC5×C112⋊C3C22
FrattiniC1G
Fitting, socleC2×C5×C112D3
LCSG ▷ C5×C112⋊C3
UCSC1 ◁ C2

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C5⋊#10624391, C2×C3×C5⋊#10624391, C2×C3⋊(C5⋊#10624391), …
maximal normal subgroup ofC2×C3×C5⋊#10624391, C2×C5⋊(#10624391⋊C5), C2×C5×C5⋊#10624391
maximal quotient ofC2×C5⋊#14546095, D3×C5⋊#10624391, C2×C3×C5⋊#10624391, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 176);