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D33⋊D39 #19104232

order5148
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD33⋊D39

Splittings

Fitting, socle, derived, HallC32×C11×C13 ⋊ C22
HallC11×C13 ⋊ D32
HallC32×C13 ⋊ C2×D11
HallC32×C11 ⋊ C2×D13
SylowC13 ⋊ (C3⋊D3)⋊D11
SylowC11 ⋊ D3×D39
SylowC32 ⋊ D11×D13

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C11×C13C22
LCSG ▷ C32×C11×C13
UCSC1

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,3^2,11,13|c^a=c^2,d^a=d^2,f^a=f^12,d^b=d^2,e^b=e^10

Conjugacy classes & character table

363 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C3⋊AGL(1,𝔽11))⋊D39, C5×D33⋊D39, D33⋊D195, …
maximal normal subgroup of(C3⋊AGL(1,𝔽11))⋊D39, C5×D33⋊D39, C7×D33⋊D39
maximal quotient ofC5×D33⋊D39, D33⋊D195, #38788243, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 108);