Finite Group Databasebeta

← Prev (#37528324) Next (#37528326) →

C2×C7×D825 #37528325

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

Aliases

direct productC2×C7×D825
unambiguous semidirect product(C2×C3)⋊(C7×D275)
unambiguous semidirect product(C2×C11)⋊(C7×D75)
unambiguous semidirect product(C2×C25)⋊(C7×D33)

Splittings

FittingC2×C3×C7×C11×C25 ⋊ C2
derived, HallC3×C11×C25 ⋊ C22×C7
HallC3×C7×C11×C25 ⋊ C22
HallC7×C11×C25 ⋊ C2×D3
HallC3×C7×C25 ⋊ C2×D11
HallC11×C25 ⋊ C2×D3×C7
HallC3×C7×C11 ⋊ C2×D25
HallC7×C25 ⋊ C2×D33
HallC7×C11 ⋊ C2×D75
HallC3×C25 ⋊ C2×C7×D11
HallC3×C11 ⋊ C2×C7×D25
SylowC25 ⋊ C2×C7×D33
HallC3×C7 ⋊ C2×D275
SylowC11 ⋊ C2×C7×D75
SylowC3 ⋊ C2×C7×D275

Subgroups

subgroupG/H
center, hypercenterC2×C7D825
commutator, cosocle, hypocenterC3×C11×C25C22×C7
FrattiniC5C2×C7×D165
FittingC2×C3×C7×C11×C25C2
socleC2×C3×C5×C7×C11D5
LCSG ▷ C3×C11×C25
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 11550

A minimal faithful permutation representation — 2 generators on 48 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,15)(14,18)(16,21)(17,24)(19,27)(20,26)(22,23)(25,31)(28,32)(29,33)(30,35)(34,36)(38,39)(40,41,42,43,44,45,46);(1,2,4,6,8,10,11,9,7,5,3)(12,32,23,35,20,18,25,16,34,15,27,17,33,29,24,19,13,36,21,31,14,26,30,22,28)(37,38,39)(47,48)

Conjugacy classes & character table

5796 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 136);