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C5×#14559049 #27130848

order12100
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#14559049

Splittings

derived#10597245 ⋊ C4×C5
HallC5×#10597245 ⋊ C4
SylowC112 ⋊ C5×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C5#11925890
commutator, hypocenter#10597245C4×C5
FrattiniC2C5×#11925890
Fitting, socleC2×C5×C112D5
prime radicalC2×C5×#10597245C2
cosocleC2×#10597245C2×C5
LCSG ▷ #10597245
UCSC1 ◁ C2×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

310 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×#14559049, C5×C3⋊#14559049
maximal normal subgroup ofC3×C5×#14559049
maximal quotient ofC3×C5×#14559049, C5×C3⋊#14559049

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 127);