Finite Group Databasebeta

← Prev (#41032009) Next (#41032011) →

C7×D5×D195 #41032010

order27300
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D5×D195
unambiguous semidirect product(C3×D5)⋊(C7×D65)
unambiguous semidirect product(C5×D5)⋊(C7×D39)
unambiguous semidirect product(D5×C13)⋊(C7×D15)

Splittings

Fitting, socle, HallC3×C52×C7×C13 ⋊ C22
derived, HallC3×C52×C13 ⋊ C22×C7
HallC52×C7×C13 ⋊ C2×D3
HallC3×C52×C7 ⋊ C2×D13
HallC52×C13 ⋊ C2×D3×C7
HallC3×C7×C13 ⋊ D52
HallC52×C7 ⋊ C2×D39
HallC7×C13 ⋊ D5×D15
HallC3×C52 ⋊ C2×C7×D13
HallC3×C13 ⋊ C7×D52
SylowC52 ⋊ C2×C7×D39
HallC3×C7 ⋊ D5×D65
SylowC13 ⋊ C7×D5×D15
SylowC3 ⋊ C7×D5×D65

Subgroups

subgroupG/H
center, hypercenterC7D5×D195
commutator, cosocle, hypocenterC3×C52×C13C22×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C13C22
LCSG ▷ C3×C52×C13
UCSC1 ◁ C7

192 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 56 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) = 2730

A minimal faithful permutation representation — 2 generators on 33 points:

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

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 900);