Finite Group Databasebeta

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C2×C25×C157⋊C3 #37555478

order23550
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×C25×C157⋊C3
unambiguous semidirect product(C2×C157)⋊(C3×C25)
unambiguous semidirect product(C2×C25×C157)⋊C3

Splittings

Fitting, HallC2×C25×C157 ⋊ C3
derived, SylowC157 ⋊ C2×C3×C25
HallC25×C157 ⋊ C2×C3
HallC2×C157 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25C157⋊C3
commutator, hypocenterC157C2×C3×C25
FrattiniC5C2×C5×C157⋊C3
FittingC2×C25×C157C3
socleC2×C5×C157C3×C5
prime radicalC2×C5×C157⋊C3C5
cosocleC5×C157C2×C3×C5
LCSG ▷ C157
UCSC1 ◁ C2×C25

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7850

Conjugacy classes & character table

2750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23550, 2);