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C3×D5×C11×D13 #22575132

order8580
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×C11×D13

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C22
derived, HallC5×C13 ⋊ C22×C3×C11
HallC5×C11×C13 ⋊ C22×C3
HallC3×C11×C13 ⋊ C2×D5
HallC3×C5×C13 ⋊ C22×C11
HallC3×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C3×D5
HallC5×C11 ⋊ C2×C3×D13
HallC3×C13 ⋊ C2×D5×C11
HallC3×C5 ⋊ C2×C11×D13
SylowC13 ⋊ C2×C3×D5×C11
SylowC5 ⋊ C2×C3×C11×D13

Subgroups

subgroupG/H
center, hypercenterC3×C11D5×D13
commutator, hypocenterC5×C13C22×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22
LCSG ▷ C5×C13
UCSC1 ◁ C3×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1056 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD5×C11×D13⋊C9, C9×D5×C11×D13, C3×D5×C11×D13⋊C3, …
maximal normal subgroup ofD5×C11×D13⋊C9, C9×D5×C11×D13, C3×D5×C11×D13⋊C3, …
maximal quotient ofC9×D5×C11×D13, C32×D5×C11×D13, C3×C11×D13×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 104);