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C5×#19153512 #43274166

order28860
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#19153512

Splittings

Fitting, socle, HallC5×C13×C37 ⋊ C3×C4
derived, HallC13×C37 ⋊ C3×C4×C5
HallC5×#14515322 ⋊ C3
HallC5×C13×C37⋊C3 ⋊ C4
Hall#14515322 ⋊ C3×C5
HallC13×C37⋊C3 ⋊ C4×C5
HallC5×C37⋊C3 ⋊ #261
HallC5×C37 ⋊ C3×#261
HallC37⋊C3 ⋊ C5×#261
HallC5×C13 ⋊ Dic37⋊C3
SylowC37 ⋊ C3×C5×#261
SylowC13 ⋊ C5×Dic37⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#19153512
commutator, hypocenterC13×C37C3×C4×C5
FrattiniC1G
Fitting, socleC5×C13×C37C3×C4
prime radicalC5×D13×C37⋊C3C2
cosocleD13×C37C2×C3×C5
LCSG ▷ C13×C37
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2405

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28860, 71);