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C2×D5×(C112⋊C3)⋊C5 #49137361

order36300
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×(C112⋊C3)⋊C5
unambiguous semidirect productC5⋊(C22×(C112⋊C3)⋊C5)
unambiguous semidirect product(C2×C5)⋊(C2×(C112⋊C3)⋊C5)
unambiguous semidirect product(C2×D5×C112⋊C3)⋊C5
unambiguous semidirect product(C2×D5×#10597243)⋊C3

Splittings

Fitting, socleC2×C5×C112 ⋊ C2×C3×C5
derivedC5×C112 ⋊ C22×C3×C5
HallC2×D5×#10597243 ⋊ C3
HallC5×(C112⋊C3)⋊C5 ⋊ C22
HallC5×#10597243 ⋊ C22×C3
HallC112⋊C3 ⋊ C2×C5×D5
SylowC112 ⋊ C2×C3×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2D5×(C112⋊C3)⋊C5
commutator, cosocle, hypocenterC5×C112C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C112C2×C3×C5
LCSG ▷ C5×C112
UCSC1 ◁ C2

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 497);