Finite Group Databasebeta

← Prev (#46776391) Next (#46776393) →

C3×Dic2795 #46776392

order33540
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic2795

Splittings

derived, HallC5×C13×C43 ⋊ C3×C4
HallC3×C5×C13×C43 ⋊ C4
HallC3×C13×C43 ⋊ Dic5
HallC3×C5×C43 ⋊ Dic13
HallC13×C43 ⋊ C3×Dic5
HallC5×C43 ⋊ C3×Dic13
HallC3×C5×C13 ⋊ Dic43
HallC3×C43 ⋊ Dic65
HallC5×C13 ⋊ C3×Dic43
SylowC43 ⋊ C3×Dic65
HallC3×C13 ⋊ Dic215
HallC3×C5 ⋊ Dic559
SylowC13 ⋊ C3×Dic215
SylowC5 ⋊ C3×Dic559

Subgroups

subgroupG/H
center, hypercenterC2×C3D2795
commutator, hypocenterC5×C13×C43C3×C4
FrattiniC2C3×D2795
Fitting, socle, prime radicalC2×C3×C5×C13×C43C2
cosocleC2×C5×C13×C43C2×C3
LCSG ▷ C5×C13×C43
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33540

Conjugacy classes & character table

8394 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 12);