Finite Group Databasebeta

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C11×#15668736 #44568498

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#15668736

Splittings

derived, HallC5×C72 ⋊ C3×C4×C11
HallC7×C11×Dic35 ⋊ C3
HallC5×C11×#3861 ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC11×#3861 ⋊ Dic5
HallC7×Dic35 ⋊ C3×C11
HallC5×#3861 ⋊ C4×C11
HallC72×C11 ⋊ C3×Dic5
Hall#3861 ⋊ C11×Dic5
HallC5×C11 ⋊ #10596873
SylowC72 ⋊ C3×C11×Dic5
SylowC5 ⋊ C11×#10596873

Subgroups

subgroupG/H
center, hypercenterC2×C11C5⋊#64423
commutator, hypocenterC5×C72C3×C4×C11
FrattiniC2C11×C5⋊#64423
Fitting, socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C11×#3861C2
cosocleC2×C5×C72C2×C3×C11
LCSG ▷ C5×C72
UCSC1 ◁ C2×C11

144 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1540

Conjugacy classes & character table

1210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 200);