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C25×C3⋊(C11⋊D11) #31827602

order18150
automorphism?
homologyAbelianization (H1) = C2×C25 · Schur multiplier (H2) = C11

Aliases

direct productC25×C3⋊(C11⋊D11)
unambiguous semidirect productC3⋊(C25×C11⋊D11)

Splittings

Fitting, HallC3×C112×C25 ⋊ C2
derived, HallC3×C112 ⋊ C2×C25
HallC112×C25 ⋊ D3
SylowC112 ⋊ D3×C25
HallC3×C25 ⋊ C11⋊D11
SylowC3 ⋊ C25×C11⋊D11

Subgroups

subgroupG/H
center, hypercenterC25C3⋊(C11⋊D11)
commutator, hypocenterC3×C112C2×C25
FrattiniC5C5×C3⋊(C11⋊D11)
FittingC3×C112×C25C2
socle, cosocleC3×C5×C112C2×C5
prime radicalC5×C3⋊(C11⋊D11)C5
LCSG ▷ C3×C112
UCSC1 ◁ C25

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9075

Conjugacy classes & character table

4575 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C25×C11⋊D11, D11×C25×D33, D25×C3⋊(C11⋊D11), …
maximal normal subgroup ofD3×C25×C11⋊D11, D11×C25×D33, D25×C3⋊(C11⋊D11), …
maximal quotient ofC25×C3⋊(C11⋊Dic11), C2×C25×C3⋊(C11⋊D11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 86);