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C11×D15⋊(C7⋊D7) #44568921

order32340
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C7

Aliases

direct productC11×D15⋊(C7⋊D7)
unambiguous semidirect productD15⋊(C11×C7⋊D7)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C22
derived, HallC3×C5×C72 ⋊ C22×C11
HallC5×C72×C11 ⋊ C2×D3
HallC3×C72×C11 ⋊ C2×D5
HallC72×C11 ⋊ D3×D5
HallC5×C72 ⋊ C2×D3×C11
HallC3×C5×C11 ⋊ C2×C7⋊D7
HallC3×C72 ⋊ C2×D5×C11
HallC5×C11 ⋊ D3×C7⋊D7
SylowC72 ⋊ D3×D5×C11
HallC3×C11 ⋊ D5×C7⋊D7
HallC3×C5 ⋊ C2×C11×C7⋊D7
SylowC5 ⋊ D3×C11×C7⋊D7
SylowC3 ⋊ D5×C11×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC11D15⋊(C7⋊D7)
commutator, cosocle, hypocenterC3×C5×C72C22×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C3×C5×C72
UCSC1 ◁ C11

400 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 8085

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(18,19)(27,28,30,32,33,31,29);(13,14)(15,16)(17,18,19)(21,22)(23,24)(25,26)(28,29)(30,31)(32,33);(20,21,23,25,26,24,22)

Conjugacy classes & character table

2508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 623);