Finite Group Databasebeta

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C5×(#92150⋊C3)⋊C5 #49137339

order36300
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×(#92150⋊C3)⋊C5
unambiguous semidirect product(#92150⋊C3)⋊C52
unambiguous semidirect product(#92150⋊C5)⋊(C3×C5)
unambiguous semidirect product(C5×#92150⋊C3)⋊C5
unambiguous semidirect product(C5×#92150⋊C5)⋊C3

Splittings

Fitting, socleC5×C112 ⋊ C3×C4×C5
derived, SylowC112 ⋊ C3×C4×C52
HallC5×#92150⋊C5 ⋊ C3
HallC5×(C112⋊C3)⋊C5 ⋊ C4
HallC5×#10597243 ⋊ C3×C4
Hall#92150⋊C3 ⋊ C52
Hall#92150 ⋊ C3×C52
HallC112⋊C3 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC5(#92150⋊C3)⋊C5
commutator, hypocenterC112C3×C4×C52
FrattiniC1G
Fitting, socleC5×C112C3×C4×C5
prime radicalC5×((C11⋊D11)⋊C3)⋊C5C2
cosocleC11⋊D11C2×C3×C52
LCSG ▷ C112
UCSC1 ◁ C5

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 475);