Finite Group Databasebeta

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C13×(C151⋊C3)⋊C4 #37555538

order23556
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×(C151⋊C3)⋊C4
unambiguous semidirect product(C151⋊C3)⋊(C4×C13)
unambiguous semidirect productDic151⋊(C3×C13)

Splittings

derived, SylowC151 ⋊ C3×C4×C13
HallC13×Dic151 ⋊ C3
HallC13×C151⋊C3 ⋊ C4
HallC13×C151 ⋊ C3×C4
HallDic151 ⋊ C3×C13
HallC151⋊C3 ⋊ C4×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D151⋊C3
commutator, hypocenterC151C3×C4×C13
FrattiniC2C13×D151⋊C3
Fitting, socleC2×C13×C151C2×C3
prime radicalC2×C13×C151⋊C3C2
cosocleC2×C151C2×C3×C13
LCSG ▷ C151
UCSC1 ◁ C2×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7852

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23556, 13);