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D39⋊D33 #19104229

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

Aliases

unambiguous semidirect productD39⋊D33

Splittings

Fitting, socle, derived, HallC32×C11×C13 ⋊ C22
HallC11×C13 ⋊ D32
HallC32×C13 ⋊ C2×D11
HallC32×C11 ⋊ C2×D13
SylowC13 ⋊ D3×D33
SylowC11 ⋊ (C3⋊D3)⋊D13
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|d^a=d^2,f^a=f^12,c^b=c^2,d^b=d^2,e^b=e^10

Conjugacy classes & character table

360 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD39⋊(C3⋊AGL(1,𝔽11)), C5×D39⋊D33, D39⋊D165, …
maximal normal subgroup ofD39⋊(C3⋊AGL(1,𝔽11)), C5×D39⋊D33, C7×D39⋊D33
maximal quotient ofC5×D39⋊D33, D39⋊D165, #38788246, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 105);