Finite Group Databasebeta

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C4×C13×C101⋊C5 #39910947

order26260
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×C101⋊C5
unambiguous semidirect product(C4×C101)⋊(C5×C13)
unambiguous semidirect product(C4×C13×C101)⋊C5

Splittings

Fitting, HallC4×C13×C101 ⋊ C5
derived, SylowC101 ⋊ C4×C5×C13
HallC13×C101 ⋊ C4×C5
HallC4×C101 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC4×C13C101⋊C5
commutator, hypocenterC101C4×C5×C13
FrattiniC2C2×C13×C101⋊C5
FittingC4×C13×C101C5
socleC2×C13×C101C2×C5
prime radicalC2×C13×C101⋊C5C2
cosocleC2×C101C2×C5×C13
LCSG ▷ C101
UCSC1 ◁ C4×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5252

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26260, 2);