Finite Group Databasebeta

← Prev (#37528708) Next (#37528710) →

C7×D33⋊(C5⋊D5) #37528709

order23100
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC7×D33⋊(C5⋊D5)
unambiguous semidirect productD33⋊(C7×C5⋊D5)

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C22
derived, HallC3×C52×C11 ⋊ C22×C7
HallC52×C7×C11 ⋊ C2×D3
HallC3×C52×C7 ⋊ C2×D11
HallC52×C11 ⋊ C2×D3×C7
HallC3×C7×C11 ⋊ C2×C5⋊D5
HallC52×C7 ⋊ D3×D11
HallC7×C11 ⋊ D3×C5⋊D5
HallC3×C52 ⋊ C2×C7×D11
HallC3×C11 ⋊ C2×C7×C5⋊D5
SylowC52 ⋊ D3×C7×D11
HallC3×C7 ⋊ D11×C5⋊D5
SylowC11 ⋊ D3×C7×C5⋊D5
SylowC3 ⋊ C7×D11×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC7D33⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52×C11C22×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C52×C11
UCSC1 ◁ C7

320 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 31
transitive degreeμt(G) = 5775

A minimal faithful permutation representation — 3 generators on 31 points:

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

Conjugacy classes & character table

1659 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 520);