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C2×C3×D905 #24925852

order10860
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D905
unambiguous semidirect product(C2×C5)⋊(C3×D181)

Splittings

Fitting, socleC2×C3×C5×C181 ⋊ C2
derived, HallC5×C181 ⋊ C22×C3
HallC3×C5×C181 ⋊ C22
HallC3×C181 ⋊ C2×D5
SylowC181 ⋊ C2×C3×D5
HallC3×C5 ⋊ C2×D181
SylowC5 ⋊ C2×C3×D181

Subgroups

subgroupG/H
center, hypercenterC2×C3D905
commutator, cosocle, hypocenterC5×C181C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C181C2
LCSG ▷ C5×C181
UCSC1 ◁ C2×C3

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2724 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊(#13108656⋊C2), C2×C9×D905, C2×C3×C5⋊(D181⋊C3), …
maximal normal subgroup ofC2×C5⋊(#13108656⋊C2), C2×C9×D905, C2×C3×C5⋊(D181⋊C3), …
maximal quotient ofC2×C9×D905, C3×D3×D905, C2×C32×D905, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10860, 68);