Finite Group Databasebeta

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C2×C25×C3⋊(C11⋊D11) #49137202

order36300
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C25×C3⋊(C11⋊D11)
unambiguous semidirect product(C2×C3)⋊(C25×C11⋊D11)

Splittings

FittingC2×C3×C112×C25 ⋊ C2
derived, HallC3×C112 ⋊ C22×C25
HallC3×C112×C25 ⋊ C22
HallC112×C25 ⋊ C2×D3
SylowC112 ⋊ C2×D3×C25
HallC3×C25 ⋊ C2×C11⋊D11
SylowC3 ⋊ C2×C25×C11⋊D11

Subgroups

subgroupG/H
center, hypercenterC2×C25C3⋊(C11⋊D11)
commutator, hypocenterC3×C112C22×C25
FrattiniC5C2×C5×C3⋊(C11⋊D11)
FittingC2×C3×C112×C25C2
socleC2×C3×C5×C112C2×C5
prime radicalC2×C5×C3⋊(C11⋊D11)C5
cosocleC3×C5×C112C22×C5
LCSG ▷ C3×C112
UCSC1 ◁ C2×C25

420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18150

Conjugacy classes & character table

9150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 338);