Finite Group Databasebeta

← Prev (#37564008) Next (#37564010) →

C2×C5×D1209 #37564009

order24180
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1209
unambiguous semidirect product(C2×C3)⋊(C5×D403)
unambiguous semidirect product(C2×C13)⋊(C5×D93)

Splittings

Fitting, socleC2×C3×C5×C13×C31 ⋊ C2
derived, HallC3×C13×C31 ⋊ C22×C5
HallC3×C5×C13×C31 ⋊ C22
HallC5×C13×C31 ⋊ C2×D3
HallC3×C5×C31 ⋊ C2×D13
HallC13×C31 ⋊ C2×C5×D3
HallC3×C5×C13 ⋊ C2×D31
HallC5×C31 ⋊ C2×D39
HallC3×C31 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×D93
HallC3×C13 ⋊ C2×C5×D31
SylowC31 ⋊ C2×C5×D39
HallC3×C5 ⋊ C2×D403
SylowC13 ⋊ C2×C5×D93
SylowC3 ⋊ C2×C5×D403

Subgroups

subgroupG/H
center, hypercenterC2×C5D1209
commutator, cosocle, hypocenterC3×C13×C31C22×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C31C2
LCSG ▷ C3×C13×C31
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 54
transitive degreeμt(G) = 12090

A minimal faithful permutation representation — 2 generators on 54 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(46,47)(48,49,50,51,52);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(32,33,35,37,39,41,43,44,42,40,38,36,34)(45,46,47)(53,54)

Conjugacy classes & character table

6060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 308);