Finite Group Databasebeta

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C2×C25×C163⋊C3 #37587337

order24450
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×C25×C163⋊C3
unambiguous semidirect product(C2×C163)⋊(C3×C25)
unambiguous semidirect product(C2×C25×C163)⋊C3

Splittings

Fitting, HallC2×C25×C163 ⋊ C3
derived, SylowC163 ⋊ C2×C3×C25
HallC25×C163 ⋊ C2×C3
HallC2×C163 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25C163⋊C3
commutator, hypocenterC163C2×C3×C25
FrattiniC5C2×C5×C163⋊C3
FittingC2×C25×C163C3
socleC2×C5×C163C3×C5
prime radicalC2×C5×C163⋊C3C5
cosocleC5×C163C2×C3×C5
LCSG ▷ C163
UCSC1 ◁ C2×C25

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8150

Conjugacy classes & character table

2850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24450, 2);