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D33⋊D55 #20300117

order7260
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD33⋊D55

Splittings

Fitting, socle, derived, HallC3×C5×C112 ⋊ C22
HallC5×C112 ⋊ C2×D3
HallC3×C112 ⋊ C2×D5
SylowC112 ⋊ D3×D5
HallC3×C5 ⋊ D112
SylowC5 ⋊ D33⋊D11
SylowC3 ⋊ D11×D55

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C112C22
LCSG ▷ C3×C5×C112
UCSC1

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

507 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14546095⋊D5, D99⋊D55, #36345210, …
maximal normal subgroup ofC3×D33⋊D55, (C3⋊AGL(1,𝔽11))⋊D55, #49137497, …
maximal quotient ofD99⋊D55, C3×D33⋊D55, D33⋊D165, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 217);