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#11927415⋊C5 #20259100

order6100
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#11927415⋊C5

Splittings

Fitting, socle, derivedC5×C61 ⋊ C4×C5
HallC5×C61⋊C5 ⋊ C4
SylowC61 ⋊ C5×Dic5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C61C4×C5
LCSG ▷ C5×C61
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,5,2,5,61|a^2=c,d^a=d^4,e^a=e^50,e^b=e^9,e^c=e^60

Conjugacy classes & character table

55 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#11927415⋊C3)⋊C5, C3×#11927415⋊C5, C3⋊(#11927415⋊C5)
maximal normal subgroup of(#11927415⋊C3)⋊C5, C3×#11927415⋊C5
maximal quotient ofC3×#11927415⋊C5, C3⋊(#11927415⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6100, 37);