Finite Group Databasebeta

← Prev (#37590592) Next (#37590594) →

C11×C17×Dic33 #37590593

order24684
automorphism?
homologyAbelianization (H1) = C4×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×Dic33
unambiguous semidirect productC3⋊(C11×C17×Dic11)
unambiguous semidirect productC11⋊(C11×Dic3×C17)

Splittings

derivedC3×C11 ⋊ C4×C11×C17
HallC3×C112×C17 ⋊ C4
HallC112×C17 ⋊ Dic3
HallC3×C112 ⋊ C4×C17
SylowC112 ⋊ Dic3×C17
HallC3×C17 ⋊ C11×Dic11
SylowC3 ⋊ C11×C17×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C11×C17D33
commutator, hypocenterC3×C11C4×C11×C17
FrattiniC2C11×C17×D33
Fitting, socle, prime radicalC2×C3×C112×C17C2
cosocleC2×C3×C11C2×C11×C17
LCSG ▷ C3×C11
UCSC1 ◁ C2×C11×C17

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2244

Conjugacy classes & character table

6732 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24684, 39);