Finite Group Databasebeta

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C5×#18012819 #37563744

order24180
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#18012819

Splittings

derived, HallC13×C31 ⋊ C3×C4×C5
HallC5×Dic403 ⋊ C3
HallC5×#11925882 ⋊ C4
HallC5×C13×C31 ⋊ C3×C4
HallDic403 ⋊ C3×C5
Hall#11925882 ⋊ C4×C5
HallC5×C31 ⋊ Dic13⋊C3
HallC5×C13 ⋊ (C31⋊C3)⋊C4
SylowC31 ⋊ C5×Dic13⋊C3
SylowC13 ⋊ C5×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5#14559030
commutator, hypocenterC13×C31C3×C4×C5
FrattiniC2C5×#14559030
Fitting, socleC2×C5×C13×C31C2×C3
prime radicalC2×C5×#11925882C2
cosocleC2×C13×C31C2×C3×C5
LCSG ▷ C13×C31
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8060

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 43);