Finite Group Databasebeta

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C3×C29×Dic95 #45683244

order33060
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×C29×Dic95

Splittings

derived, HallC5×C19 ⋊ C3×C4×C29
HallC3×C5×C19×C29 ⋊ C4
HallC5×C19×C29 ⋊ C3×C4
HallC3×C19×C29 ⋊ Dic5
HallC19×C29 ⋊ C3×Dic5
HallC3×C5×C29 ⋊ Dic19
HallC3×C5×C19 ⋊ C4×C29
HallC5×C29 ⋊ C3×Dic19
HallC3×C19 ⋊ Dic5×C29
SylowC19 ⋊ C3×Dic5×C29
HallC3×C5 ⋊ C29×Dic19
SylowC5 ⋊ C3×C29×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29D95
commutator, hypocenterC5×C19C3×C4×C29
FrattiniC2C3×C29×D95
Fitting, socle, prime radicalC2×C3×C5×C19×C29C2
cosocleC2×C5×C19C2×C3×C29
LCSG ▷ C5×C19
UCSC1 ◁ C2×C3×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33060

Conjugacy classes & character table

8526 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 8);