Finite Group Databasebeta

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C3×C5×Dic377 #36383075

order22620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic377

Splittings

derived, HallC13×C29 ⋊ C3×C4×C5
HallC3×C5×C13×C29 ⋊ C4
HallC5×C13×C29 ⋊ C3×C4
HallC3×C13×C29 ⋊ C4×C5
HallC3×C5×C29 ⋊ Dic13
HallC3×C5×C13 ⋊ Dic29
HallC5×C29 ⋊ C3×Dic13
HallC3×C29 ⋊ C5×Dic13
HallC5×C13 ⋊ C3×Dic29
HallC3×C13 ⋊ C5×Dic29
SylowC29 ⋊ C3×C5×Dic13
SylowC13 ⋊ C3×C5×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D377
commutator, hypocenterC13×C29C3×C4×C5
FrattiniC2C3×C5×D377
Fitting, socle, prime radicalC2×C3×C5×C13×C29C2
cosocleC2×C13×C29C2×C3×C5
LCSG ▷ C13×C29
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22620

Conjugacy classes & character table

5700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22620, 5);