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C5×C11×D221 #37566469

order24310
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D221
unambiguous semidirect productC13⋊(C5×C11×D17)
unambiguous semidirect productC17⋊(C5×C11×D13)

Splittings

Fitting, socle, HallC5×C11×C13×C17 ⋊ C2
derived, HallC13×C17 ⋊ C2×C5×C11
HallC11×C13×C17 ⋊ C2×C5
HallC5×C13×C17 ⋊ C2×C11
HallC5×C11×C17 ⋊ D13
HallC5×C11×C13 ⋊ D17
HallC11×C17 ⋊ C5×D13
HallC11×C13 ⋊ C5×D17
HallC5×C17 ⋊ C11×D13
HallC5×C13 ⋊ C11×D17
SylowC17 ⋊ C5×C11×D13
SylowC13 ⋊ C5×C11×D17

Subgroups

subgroupG/H
center, hypercenterC5×C11D221
commutator, cosocle, hypocenterC13×C17C2×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C13×C17C2
LCSG ▷ C13×C17
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12155

Conjugacy classes & character table

6160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24310, 5);