Finite Group Databasebeta

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C3×Dic2015 #37563718

order24180
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic2015

Splittings

derived, HallC5×C13×C31 ⋊ C3×C4
HallC3×C5×C13×C31 ⋊ C4
HallC3×C13×C31 ⋊ Dic5
HallC3×C5×C31 ⋊ Dic13
HallC13×C31 ⋊ C3×Dic5
HallC3×C5×C13 ⋊ Dic31
HallC5×C31 ⋊ C3×Dic13
HallC3×C31 ⋊ Dic65
HallC5×C13 ⋊ C3×Dic31
HallC3×C13 ⋊ Dic155
SylowC31 ⋊ C3×Dic65
HallC3×C5 ⋊ Dic403
SylowC13 ⋊ C3×Dic155
SylowC5 ⋊ C3×Dic403

Subgroups

subgroupG/H
center, hypercenterC2×C3D2015
commutator, hypocenterC5×C13×C31C3×C4
FrattiniC2C3×D2015
Fitting, socle, prime radicalC2×C3×C5×C13×C31C2
cosocleC2×C5×C13×C31C2×C3
LCSG ▷ C5×C13×C31
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24180

Conjugacy classes & character table

6054 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 17);