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D39×D55 #22575172

order8580
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD39×D55

Splittings

Fitting, socle, derived, HallC3×C5×C11×C13 ⋊ C22
HallC5×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D5
HallC3×C5×C13 ⋊ C2×D11
HallC3×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ D3×D5
HallC5×C13 ⋊ D3×D11
HallC5×C11 ⋊ C2×D39
HallC3×C13 ⋊ C2×D55
HallC3×C11 ⋊ D5×D13
HallC3×C5 ⋊ D11×D13
SylowC13 ⋊ D3×D55
SylowC11 ⋊ D5×D39
SylowC5 ⋊ D11×D39
SylowC3 ⋊ D13×D55

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C11×C13C22
LCSG ▷ C3×C5×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

609 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD55×D117, D55×C3⋊(D13⋊C3), C3×D39×D55, …
maximal normal subgroup ofD55×C3⋊(D13⋊C3), C3×D39×D55
maximal quotient ofD55×D117, C3×D39×D55, D39×D165, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 144);