Finite Group Databasebeta

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D55⋊D111 #37567627

order24420
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD55⋊D111

Splittings

Fitting, socle, derived, HallC3×C5×C11×C37 ⋊ C22
HallC5×C11×C37 ⋊ C2×D3
HallC3×C11×C37 ⋊ C2×D5
HallC3×C5×C37 ⋊ C2×D11
HallC11×C37 ⋊ D3×D5
HallC5×C37 ⋊ D3×D11
HallC3×C5×C11 ⋊ C2×D37
HallC3×C37 ⋊ D5×D11
HallC5×C11 ⋊ C2×D111
SylowC37 ⋊ D15⋊D11
HallC3×C11 ⋊ D5×D37
HallC3×C5 ⋊ D11×D37
SylowC11 ⋊ D5×D111
SylowC5 ⋊ D11×D111
SylowC3 ⋊ D55⋊D37

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C37C22
LCSG ▷ C3×C5×C11×C37
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Polycyclic presentation:

2^2,3,5,11,37|c^a=c^2,e^a=e^10,f^a=f^36,d^b=d^4,e^b=e^10

Conjugacy classes & character table

1623 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 148);