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C5×C13⋊C3×Dic13 #23778402

order10140
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13⋊C3×Dic13

Splittings

derived, SylowC132 ⋊ C3×C4×C5
HallC5×C13×Dic13 ⋊ C3
HallC5×C13×C13⋊C3 ⋊ C4
HallC5×C132 ⋊ C3×C4
HallC13×Dic13 ⋊ C3×C5
HallC13×C13⋊C3 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5D13×C13⋊C3
commutator, hypocenterC132C3×C4×C5
FrattiniC2C5×D13×C13⋊C3
Fitting, socleC2×C5×C132C2×C3
prime radicalC2×C5×C13×C13⋊C3C2
cosocleC2×C132C2×C3×C5
LCSG ▷ C132
UCSC1 ◁ C2×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

560 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C13⋊C3×Dic13⋊C3, C3×C5×C13⋊C3×Dic13, C5×C13⋊C3×Dic39
maximal normal subgroup ofC5×C13⋊C3×Dic13⋊C3, C3×C5×C13⋊C3×Dic13
maximal quotient ofC5×Dic13×C13⋊C9, C3×C5×C13⋊C3×Dic13, C5×C13⋊C3×Dic39

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 60);